2026-08-21 7 min

Energy Calculator

Compute kinetic energy (KE = ½mv²), gravitational potential energy (PE = mgh), elastic potential energy (E = ½kx²), and total mechanical energy from mass, velocity, height, spring constant, and displacement.

Calculator

Mass(kg) Help

Mass of the object in kilograms

Velocity(m/s) Help

m/s

Velocity of the object in meters per second

Height(m) Help

Height above reference level in meters

Spring Constant(N/m) Help

N/m

Spring stiffness in newtons per meter

Displacement(m) Help

Spring compression or extension in meters

Gravity(m/s²) Help

m/s²

Gravitational acceleration (default 9.81 m/s² on Earth)

Decimal Precision

Results update live as you type

Results

Normal

Kinetic Energy

125.00J

Energy of motion (KE = ½mv²)

Potential Energy

981.00J

Gravitational potential energy (PE = mgh)

Elastic Energy

2.50J

Elastic potential energy (E = ½kx²)

Total Energy

1108.50J

Sum of all mechanical energy forms

Kinetic Energy

0.13kJ

Kinetic energy in kilojoules

Potential Energy

0.98kJ

Potential energy in kilojoules

Total Energy

1.11kJ

Total energy in kilojoules

Total Energy

3.08e-4kWh

Total energy in kilowatt-hours

Visualizations

Results Overview

125JKinetic Energy

981JPotential Energy

2.5JElastic Energy

1,109JTotal Energy

0.1JKinetic Energy

1JPotential Energy

1.1JTotal Energy

0JTotal Energy

Formula

Mechanical energy exists in three primary forms. Kinetic energy is the energy of motion, proportional to mass and the square of velocity. Gravitational potential energy is stored energy due to height above a reference level. Elastic potential energy is stored in deformed springs and elastic materials.

KE = ½mv², PE = mgh, E = ½kx²

Alternative Form

Total = KE + PE + Elastic

Variables

Symbol	Name	Unit	Description
KE	Kinetic Energy	J	Energy of motion: KE = ½mv²
PE	Potential Energy	J	Gravitational stored energy: PE = mgh
E	Elastic Energy	J	Elastic stored energy: E = ½kx²
m	Mass	kg	Mass of the object
v	Velocity	m/s	Speed of the object
g	Gravity	m/s²	Gravitational acceleration (default 9.81)
h	Height	m	Height above reference level
k	Spring Constant	N/m	Stiffness of the spring
x	Displacement	m	Spring compression or extension from equilibrium

Explanation

The principle of conservation of energy states that energy cannot be created or destroyed, only converted from one form to another. In an isolated system with no non-conservative forces (friction, air resistance), the total mechanical energy remains constant: KE₁ + PE₁ + E₁ = KE₂ + PE₂ + E₂. This means that as an object falls, its potential energy converts to kinetic energy. As a spring is compressed, work is stored as elastic energy and later converts to kinetic energy when released.

Derivation

Kinetic energy derives from the work-energy theorem: W = ΔKE. For a constant force F = ma over distance d: W = Fd = mad. Using v² = v₀² + 2ad (with v₀ = 0): d = v²/(2a). Substituting: W = ma · v²/(2a) = ½mv². Potential energy comes from W = Fd = mgh (gravity is constant near Earth). Elastic energy from Hooke's law: W = ∫₀ˣ kx dx = ½kx².

Step-by-Step Calculation

Follow each step to understand how the result is calculated from your inputs.

Step 1

Identify all input values for the three energy forms.

Mass (m):10.00 kg

Velocity (v):5.00 m/s

Height (h):10.00 m

Spring Constant (k):500.00 N/m

Displacement (x):0.10 m

Gravity (g):9.81 m/s²

Result: m = 10.00 kg, v = 5.00 m/s, h = 10.00 m, k = 500.00 N/m, x = 0.10 m, g = 9.81 m/s²

Step 2

Calculate kinetic energy using KE = ½mv².

KE = ½ × m × v²

m:10.00 kg

v:5.00 m/s

Intermediate: KE = 0.5 × 10.00 × 5.00² = 0.5 × 10.00 × 25.00

Result: KE = 125.00 J

Step 3

Calculate gravitational potential energy using PE = mgh.

PE = m × g × h

m:10.00 kg

g:9.81 m/s²

h:10.00 m

Intermediate: PE = 10.00 × 9.81 × 10.00 = 98.10 × 10.00

Result: PE = 981.00 J

Step 4

Calculate elastic potential energy using E = ½kx².

E = ½ × k × x²

k:500.00 N/m

x:0.10 m

Intermediate: E = 0.5 × 500.00 × 0.10² = 0.5 × 500.00 × 0.01

Result: E = 2.50 J

Step 5

Sum all energy forms to get total mechanical energy.

Total = KE + PE + E

KE:125.00 J

PE:981.00 J

E:2.50 J

Intermediate: Total = 125.00 + 981.00 + 2.50

Result: Total = 1108.50 J = 1.11 kJ = 3.08e-4 kWh

Step 6

Convert total energy to other common units for reference.

kJ = J/1000, kcal = J/4184, BTU = J/1055.06, kWh = J/3.6×10⁶

Total (J):1108.50 J

Intermediate: 1108.50 J → 1.11 kJ → 0.26 kcal → 1.05 BTU → 3.08e-4 kWh

Result: 1.11 kJ = 0.26 kcal = 1.05 BTU = 3.08e-4 kWh

Final Answer

125.00

Worked Examples

See how the calculator works with different scenarios.

Scenario

A 5 kg ball is dropped from a height of 20 m. Calculate the kinetic energy, potential energy, and total energy at the moment of release. Ignore air resistance.

Inputs

Mass:5 kg

Velocity:0 m/s (at release)

Height:20 m

Spring Constant:0 N/m (no spring)

Displacement:0 m

Gravity:9.81 m/s²

Calculation

KE = ½ × 5 × 0² = 0 J PE = 5 × 9.81 × 20 = 981 J E = ½ × 0 × 0² = 0 J Total = 0 + 981 + 0 = 981 J

Result

KE = 0 J, PE = 981 J, E = 0 J, Total = 981 J

Interpretation

At the moment of release, the ball has zero kinetic energy (not yet moving) and maximum potential energy (981 J). As it falls, PE converts to KE. Just before impact, nearly all 981 J of PE becomes KE, giving the ball a velocity of v = √(2gh) = √(2 × 9.81 × 20) ≈ 19.81 m/s.

Understanding Your Result

Your Result: Kinetic Energy: 125.00 J

Typical range: Everyday objects: 1-1000 J. Vehicle kinetic energy at highway speed: 300,000-800,000 J. Falling object from 100 m: 1,000-10,000 J per kg. Industrial spring energy: 10-10,000 J. Electrical energy consumed per household per day: 10-50 kWh (36-180 MJ).

What This Means

Energy is the capacity to do work. This calculator shows three forms of mechanical energy: kinetic (energy of motion), gravitational potential (energy of position), and elastic (energy of deformation). The total mechanical energy is their sum. In ideal systems without friction, this total remains constant — energy merely converts between forms.

Why It Matters

Understanding energy forms is fundamental to mechanical engineering, physics, and design. Engineers use energy analysis to size motors, design safety systems (crash barriers, springs), optimize roller coasters, predict projectile motion, and analyze any system where objects move, fall, or interact with springs. Energy conservation is one of the most powerful tools in physics.

Professional Interpretation

Energy values indicate the capacity for work in a system. High kinetic energy means high-speed impact potential (relevant for safety design). High potential energy means significant height-related risk (relevant for fall protection). Elastic energy indicates stored force in springs (relevant for mechanical systems and energy storage). The total energy determines the maximum work the system can perform.

Recommendations

•Always specify the reference level for potential energy — it is relative, not absolute
•In real systems, friction converts mechanical energy to heat — account for 5-20% losses typically
•Kinetic energy scales with v² — doubling speed quadruples KE, which is critical for safety analysis
•Elastic energy scales with x² — doubling displacement quadruples stored energy, important for spring design
•Use energy conservation to cross-check results from force-based (Newtonian) analyses

Educational Content

Introduction

Energy is one of the most fundamental concepts in all of science and engineering. It exists in many forms — kinetic, potential, thermal, chemical, nuclear, and more — and is governed by the law of conservation of energy: energy cannot be created or destroyed, only converted from one form to another. This principle, first articulated in the 19th century, underpins virtually all of modern physics, chemistry, and engineering.

Concept Explanation

Mechanical energy is the sum of kinetic energy and potential energy. Kinetic energy (KE = ½mv²) is the energy an object possesses due to its motion — it depends on mass and the square of velocity. Gravitational potential energy (PE = mgh) is the energy stored by an object due to its height above a reference point — it depends on mass, gravitational acceleration, and height. Elastic potential energy (E = ½kx²) is the energy stored when a spring or elastic material is deformed — it depends on the spring constant and the square of displacement. In an ideal system with no friction, total mechanical energy is conserved: KE₁ + PE₁ + E₁ = KE₂ + PE₂ + E₂.

Applications

▸Vehicle crash safety analysis — kinetic energy determines impact severity and energy absorption requirements

▸Roller coaster and amusement ride design — converting between PE and KE for thrill and safety

▸Seismic energy estimation — calculating energy release during earthquakes from ground motion

▸Spring-loaded mechanisms — watches, automotive suspensions, industrial actuators

▸Ballistics and projectile motion — predicting trajectories and impact energies

▸Hydroelectric power generation — converting gravitational PE of water to electrical energy

▸Pendulum and clock mechanisms — periodic conversion between KE and PE

▸Energy storage systems — flywheels (KE), pumped hydro (PE), springs (elastic)

Benefits

•Provides a universal framework applicable across all branches of engineering and physics
•Energy analysis is often simpler than force analysis for complex systems
•Conservation of energy gives powerful constraints that simplify problem-solving
•Scalar nature (no direction) makes energy easier to work with than vector quantities
•Connects mechanical systems to thermal, electrical, and chemical systems through energy conversion

Limitations

•Does not account for energy losses to friction, air resistance, or heat unless explicitly modeled
•Potential energy reference level is arbitrary — only differences in PE are physically meaningful
•Elastic energy assumes Hooke's law (linear spring) — non-linear springs require different formulas
•Relativistic effects are ignored — for objects approaching light speed, KE = (γ-1)mc² must be used
•Real springs have mass, internal friction, and fatigue — ideal spring assumptions may not hold

Best Practices

•Always define a clear reference level for potential energy (e.g., ground level, equilibrium position)
•Check units carefully — mass in kg, velocity in m/s, height in m, spring constant in N/m, displacement in m
•Use energy conservation as a sanity check — total energy in = total energy out in isolated systems
•Account for friction and air resistance in real-world applications (typically 5-20% energy loss)
•Remember that kinetic energy depends on v² — small velocity changes cause large KE changes
•For elastic energy, ensure displacement is measured from the spring's equilibrium position

Common Misconceptions

Myth: Heavier objects always have more kinetic energy.

Truth: Kinetic energy depends on both mass AND velocity. A light object moving fast can have more KE than a heavy object moving slowly. KE = ½mv² means doubling velocity has four times the effect of doubling mass.

Myth: Potential energy is fixed for an object.

Truth: Potential energy depends on the chosen reference level. A book on a table has PE relative to the floor, zero PE relative to itself, and negative PE relative to the ceiling. Only changes in PE are physically meaningful.

Myth: Energy is lost when a ball bounces.

Truth: Energy is never lost — it is converted to other forms. When a ball bounces, kinetic energy converts to elastic energy during compression, then back. Some energy always converts to heat and sound, reducing mechanical energy but total energy is conserved.

Myth: A heavier spring stores more energy for the same compression.

Truth: Elastic energy depends on the spring constant k, not mass. A stiffer spring (higher k) stores more energy for the same displacement: E = ½kx². A 1000 N/m spring compressed 1 cm stores 0.05 J, while a 100 N/m spring compressed 1 cm stores only 0.005 J.

Myth: Kinetic and potential energy are always equal.

Truth: They are equal only at specific transition points (e.g., halfway down a fall). At any other point, one dominates. At the top of a hill, PE >> KE. At the bottom, KE >> PE. Their sum (total mechanical energy) remains constant in ideal systems.

Practical Tips

•Remember: doubling velocity quadruples kinetic energy — this is why car crashes at high speed are so devastating
•Use g = 9.81 m/s² for Earth surface calculations; on the Moon use 1.62 m/s², on Mars 3.72 m/s²
•Potential energy is relative — always specify your reference height (usually ground level)
•For spring energy, displacement is from the equilibrium (unstretched) position, not from the wall
•Total energy in joules can be converted: 1 kWh = 3.6 MJ, 1 kcal = 4184 J, 1 BTU = 1055 J
•In energy conservation problems, set KE₁ + PE₁ = KE₂ + PE₂ to find unknown velocities or heights
•Use scientific notation for very large or very small energy values (e.g., 1.5e6 J instead of 1,500,000 J)

Common Mistakes

Using mass in grams instead of kilograms

The SI unit for mass in energy formulas is kilograms (kg). Convert: 500 g = 0.5 kg. Using grams gives results 1,000,000 times too large.

Forgetting to square velocity in KE = ½mv²

KE depends on v², not v. Always square the velocity: KE = ½ × m × v × v. A common mistake is writing ½mv instead of ½mv².

Using displacement from the wall instead of from equilibrium for spring energy

x in E = ½kx² is the displacement from the spring's natural (unstretched) length, not the distance from a wall or other reference.

Mixing up height and distance in PE = mgh

h is the vertical height above the reference level, not the distance along a slope. For a ramp: h = L × sin(θ), where L is ramp length and θ is the angle.

Forgetting to convert cm or mm to meters for spring displacement

Spring displacement x must be in meters. Common conversions: 5 cm = 0.05 m, 10 mm = 0.01 m. Using cm gives energy 10,000 times too large.

Assuming total mechanical energy is always conserved

Energy conservation holds only in ideal systems without friction. In real systems, some mechanical energy converts to heat (thermal energy). Always account for energy losses in practical applications.

Assumptions

This calculator makes the following assumptions to provide estimates:

No Air Resistance: The calculator ignores air drag, which can significantly reduce kinetic energy for fast-moving or low-density objects. For precise results at high speeds, aerodynamic drag must be modeled separately.

Constant Gravitational Field: Gravity is assumed constant at the given value (default 9.81 m/s²). For objects moving through large height changes (>1 km), the variation of g with altitude should be considered.

Ideal Spring (Hooke's Law): Elastic energy assumes the spring obeys Hooke's law (F = kx) with constant stiffness k. Real springs may exhibit non-linear behavior, especially near their elastic limit.

Point Mass Approximation: The object is treated as a point mass without rotational energy. For extended bodies, rotational kinetic energy (½Iω²) may be significant and is not included.

No Energy Dissipation: Energy losses due to friction, internal damping, and deformation are not modeled. In real systems, these losses reduce the total mechanical energy over time.

Limitations

Be aware of these limitations when using this calculator:

No Friction or Drag Modeling: The calculator computes ideal mechanical energy only. Friction, air resistance, and other dissipative forces that reduce mechanical energy are not included in the calculation.

No Rotational Energy: Rotational kinetic energy (½Iω²) is not calculated. For spinning or rolling objects, this form of energy can be significant and must be added separately.

No Thermal Energy: The calculator does not account for thermal energy generated by friction or deformation. In real systems, some mechanical energy always converts to heat.

No Time Dependence: The energy values represent instantaneous snapshots. The calculator does not model how energy changes over time or during energy conversion processes.

Single Reference Frame: All calculations are in the same reference frame. Relative motion between reference frames requires relativistic corrections at high velocities.

Frequently Asked Questions

Answers to common questions about this calculator.

What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion, calculated as KE = ½mv² where m is mass (kg) and v is velocity (m/s). The SI unit is the joule (J). Kinetic energy is always non-negative and increases with the square of velocity — doubling speed quadruples KE.

What is gravitational potential energy?

Gravitational potential energy is the energy stored by an object due to its position in a gravitational field, calculated as PE = mgh where m is mass, g is gravitational acceleration, and h is height above a reference level. It is relative to the chosen reference point and is measured in joules.

What is elastic potential energy?

Elastic potential energy is the energy stored when a spring or elastic material is deformed (compressed or stretched), calculated as E = ½kx² where k is the spring constant (N/m) and x is displacement from equilibrium (m). It is proportional to the square of displacement.

What is total mechanical energy?

Total mechanical energy is the sum of kinetic energy, gravitational potential energy, and elastic potential energy: Total = KE + PE + E. In an ideal system with no friction, this total is conserved (constant) as energy converts between forms.

What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, only converted from one form to another. In an isolated system, total energy remains constant. This is one of the most fundamental principles in physics, applicable to all forms of energy.

How does energy convert between kinetic and potential?

When an object falls, gravitational PE converts to KE (it speeds up). When thrown upward, KE converts to PE (it slows down). At the highest point, KE = 0 and PE is maximum. At the lowest point, PE = 0 (relative to that level) and KE is maximum. In ideal systems, KE + PE = constant.

What happens to energy in a car crash?

The car's kinetic energy (KE = ½mv²) must be absorbed during the crash. It converts to: deformation energy (crumpling metal), thermal energy (heat from friction), sound energy (crash noise), and some remaining kinetic energy of the passengers. Car crumple zones are designed to maximize energy absorption over distance, reducing peak forces.

Why does kinetic energy depend on v² not v?

This comes from the work-energy theorem. To accelerate an object from rest, work W = Fd. Using F = ma and v² = 2ad, we get W = ½mv². The v² dependence means that energy grows much faster than speed — this is why high-speed impacts are so much more destructive than low-speed ones.

What units are used for energy?

The SI unit is the joule (J). Common conversions: 1 kJ = 1000 J, 1 cal = 4.184 J, 1 kcal = 4184 J, 1 BTU = 1055.06 J, 1 kWh = 3.6 MJ, 1 eV = 1.602 × 10⁻¹⁹ J. The calorie is commonly used in food and chemistry; BTU in heating/cooling; kWh in electricity billing.

How is energy calculated for a falling object?

At any height h during free fall: PE = mgh (remaining height), KE = ½mv² (current speed). By conservation: mgh_total = ½mv² + mgh_current. The velocity at height h is v = √(2g(h_total - h)). At the bottom (h = 0): all PE converts to KE.

What is the reference level for potential energy?

The reference level (h = 0) is the point where PE = 0, chosen by the problem solver. Common choices: ground level, the lowest point in the system, or the spring's equilibrium position. Only differences in PE matter physically, so the choice of reference doesn't affect energy conservation equations.

Does a moving object always have kinetic energy?

Yes, any object with non-zero velocity has kinetic energy (KE = ½mv² > 0). The only exception is an object at rest (v = 0), which has KE = 0. Kinetic energy is always non-negative — there is no such thing as negative kinetic energy.

How much energy does a 1 kg object have when falling from 10 m?

PE = mgh = 1 × 9.81 × 10 = 98.1 J. At the bottom, all this PE converts to KE: ½mv² = 98.1 J, giving v = √(2 × 98.1 / 1) = √196.2 ≈ 14.0 m/s (about 50 km/h).

What is the difference between energy and work?

Work is the process of energy transfer; energy is the capacity to do work. When you do work on an object (push it), you transfer energy to it. The work-energy theorem states W_net = ΔKE — net work equals the change in kinetic energy. Work is measured in joules, same as energy.

Can energy be negative?

Kinetic energy (½mv²) is always non-negative. Potential energy can be negative if the object is below the reference level (h < 0). Elastic energy is always non-negative. Total mechanical energy can be negative if PE is negative and larger in magnitude than KE + E, though this is uncommon in practice.

What is the energy of a 1000 kg car at 30 m/s?

KE = ½ × 1000 × 30² = 450,000 J = 450 kJ. This is equivalent to 107.6 kcal or 426.7 BTU. At 30 m/s (108 km/h), this energy could lift the car to a height of h = KE/(mg) = 450,000/(1000 × 9.81) ≈ 45.9 m.

What is the energy stored in a compressed spring?

E = ½kx². For a car suspension spring (k ≈ 25,000 N/m) compressed 10 cm: E = ½ × 25,000 × 0.1² = 125 J. For a garage door spring (k ≈ 10,000 N/m) compressed 20 cm: E = ½ × 10,000 × 0.2² = 200 J.

How does energy conservation apply to a pendulum?

At the highest point of swing, all energy is PE (KE = 0). At the lowest point, all energy is KE (PE = 0). At intermediate points, KE + PE = total energy (constant). The velocity at any angle θ from vertical is v = √(2gL(cos θ - cos θ_max)), where L is length and θ_max is the maximum angle.

What is the maximum height a ball can reach if thrown at 20 m/s?

Using energy conservation: ½mv² = mgh → h = v²/(2g) = 20²/(2 × 9.81) = 400/19.62 ≈ 20.39 m. At this height, all kinetic energy has converted to potential energy. The ball momentarily stops before falling back down.

How much energy is needed to lift a 70 kg person up 3 meters?

PE = mgh = 70 × 9.81 × 3 = 2060.1 J ≈ 2.06 kJ. This is about 0.49 kcal or roughly the energy in a small apple. The equivalent power needed to climb in 10 seconds is P = W/t = 206 W — within normal human power output capability.

What is the energy equivalence of 1 kWh?

1 kWh = 1000 W × 3600 s = 3,600,000 J = 3.6 MJ. This is approximately 860 kcal or 3412 BTU. A typical household uses 10-30 kWh per day (36-108 MJ). One gallon of gasoline contains about 33.7 kWh (121 MJ) of energy.

How does gravity affect energy calculations on different planets?

Gravity varies by location: Earth 9.81 m/s², Moon 1.62 m/s², Mars 3.72 m/s², Jupiter 24.79 m/s². Potential energy PE = mgh scales with g, so the same object at the same height has less PE on the Moon and more on Jupiter. Kinetic energy is independent of gravity.

What is the relationship between energy and power?

Power is the rate of energy transfer: P = dE/dt. Energy (J) is the total amount; power (W) is how fast it is delivered. A 100W light bulb uses 100 J per second. Over one hour it uses 100 × 3600 = 360,000 J = 360 kJ = 0.1 kWh.

How does energy apply to food and nutrition?

Food energy is measured in kilocalories (kcal, often called "Calories" with capital C). 1 kcal = 4184 J. A typical diet of 2000 kcal/day = 8.37 MJ/day. The body converts chemical energy in food to mechanical energy (movement), thermal energy (body heat), and other forms. Efficiency is about 20-25% for mechanical work.

What is the energy of a earthquake?

Earthquake energy is measured on the Richter scale. A magnitude 5 earthquake releases about 2 × 10¹² J (2 TJ). A magnitude 7 releases about 2 × 10¹⁵ J (2 PJ). This is equivalent to millions of tons of TNT. The energy calculation uses seismograph measurements of ground motion.

How is elastic energy used in everyday life?

Elastic energy is used in: rubber bands (storing and releasing energy), bows and arrows (launching projectiles), trampolines (bouncing), car suspensions (absorbing shocks), mattress springs (supporting weight), retractable pens (spring mechanisms), and wound watches (coiled springs providing power).

What is the energy of a bullet?

A 9mm bullet (8 g) at 370 m/s has KE = ½ × 0.008 × 370² = 547.6 J. A rifle bullet (10 g at 900 m/s) has KE = ½ × 0.010 × 900² = 4050 J. This energy must be absorbed by the target — it determines penetration depth and damage potential.

How much energy does the Sun deliver to Earth?

The Sun delivers about 1361 W/m² at the top of the atmosphere (solar constant). After atmospheric absorption, about 1000 W/m² reaches the surface. A 1 m² solar panel at 20% efficiency generates about 200 W. Over a day, this is 200 × 8 = 1600 Wh = 1.6 kWh.

What is the total energy of the International Space Station?

The ISS has a mass of about 420,000 kg orbiting at 7.66 km/s. Its kinetic energy is KE = ½ × 420,000 × 7660² ≈ 1.23 × 10¹³ J = 12.3 TJ. This is equivalent to about 3,400 kWh or the energy released by about 3 tons of TNT.

How does energy conservation apply to a roller coaster?

At the top of the first hill (maximum height), all energy is PE. As the coaster descends, PE converts to KE (speed increases). At the bottom, KE is maximum. Subsequent hills convert KE back to PE (slowing the coaster). Without friction, the coaster could never go higher than the first hill. With friction, each hill must be lower than the previous one.

What is the kinetic energy of Earth orbiting the Sun?

Earth's mass is 5.97 × 10²⁴ kg, orbital velocity 29,780 m/s. KE = ½ × 5.97 × 10²⁴ × 29,780² ≈ 2.65 × 10³³ J. This is about 6.3 × 10²⁶ kcal or 2.5 × 10²⁷ BTU — an enormous amount of energy maintained by gravitational attraction.

How much energy is in a lightning bolt?

A typical lightning bolt transfers about 1-5 billion joules (1-5 GJ). The peak power can reach 1 terawatt (10¹² W), but the duration is only about 30 microseconds. The energy is enough to power a 100W light bulb for about 3-15 months.

What is the energy of nuclear fusion in the Sun?

The Sun converts about 4.26 million metric tons of mass to energy every second via E = mc². This produces 3.8 × 10²⁶ W of power. Over its 10-billion-year lifetime, the Sun will convert about 100 Earth masses of hydrogen to helium, releasing approximately 10⁴⁴ joules total.

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Glossary

Technical terms used in mortgage calculations explained in plain language.

Kinetic Energy (KE): The energy of motion: KE = ½mv². Always non-negative, measured in joules. Depends on mass and the square of velocity.
Potential Energy (PE): Stored energy due to position in a gravitational field: PE = mgh. Relative to a chosen reference level. Measured in joules.
Elastic Potential Energy: Energy stored in a deformed spring: E = ½kx². Proportional to spring constant and displacement squared. Measured in joules.
Total Mechanical Energy: The sum of kinetic, gravitational potential, and elastic potential energy. Conserved in ideal systems without friction.
Conservation of Energy: The principle that energy cannot be created or destroyed, only converted between forms. Total energy in an isolated system remains constant.
Joule (J): The SI unit of energy and work. 1 J = 1 N·m = 1 W·s. Named after James Prescott Joule (1818-1889).
Spring Constant (k): A measure of a spring's stiffness, in N/m. Higher k means stiffer spring, requiring more force for the same displacement.
Gravitational Acceleration (g): The acceleration due to gravity: 9.80665 m/s² on Earth's surface. Varies by location: Moon 1.62, Mars 3.72 m/s².
Work-Energy Theorem: The net work done on an object equals its change in kinetic energy: W_net = ΔKE. Bridges force analysis and energy analysis.
Conservative Force: A force where work done is path-independent. Gravity and spring forces are conservative. Friction is non-conservative.
Reference Level: The chosen height where potential energy is defined as zero. Only differences in PE are physically meaningful.
Energy Conversion: The transformation of energy from one form to another (e.g., PE → KE during free fall). Total energy is preserved.
Kilowatt-hour (kWh): A unit of energy equal to 1000 watts maintained for 1 hour. 1 kWh = 3.6 MJ. Commonly used for electrical energy billing.
British Thermal Unit (BTU): The energy needed to raise 1 pound of water by 1°F. 1 BTU = 1055.06 J. Commonly used in HVAC and heating systems.
Calorie (cal): The energy to raise 1 gram of water by 1°C at standard pressure. 1 cal = 4.184 J. The food Calorie (kcal) is 1000 cal.

Authoritative References

Trusted sources and standards referenced by this calculator.

Halliday, Resnick & Walker — Fundamentals of Physics Serway & Jewett — Physics for Scientists and Engineers Kleppner & Kolenkow — An Introduction to Mechanics NIST Reference on Constants, Units, and Uncertainty Engineering Toolbox — Energy HyperPhysics — Energy Conservation Khan Academy — Work, Energy, and Power MIT OpenCourseWare — Classical Mechanics

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Last Updated:

2026-08-21

Version:

2.0.0

References:

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