2026-08-21 14 min
Gear Torque Calculator
Compute output torque T₂ = T₁ × GR × η for gear systems with efficiency losses. Calculates output speed, input/output power, and supports preset gear ratios.
Calculator
Input Torque(N\u00B7m) Help
N\u00B7m
Torque applied to the driving gear
Input Speed(RPM) Help
RPM
Rotational speed of the driving gear
Gear Ratio (N\u2082/N\u2081) Help
Ratio of driven to driving gear teeth
Preset Ratios
Select a common gear ratio
Efficiency(%) Help
%
Gear mesh efficiency (typically 90-99%)
Decimal Precision
Number of decimal places in results
Results update live as you type
Results
Optimal
Output Torque (T₂)
285.00N·m
T₂ = 100 × 3 × 0.95 = 285.00
Output Speed
333.33RPM
ω₂ = 1000 / 3 = 333.33
Input Power
10471.98W
P₁ = T₁ × ω₁
Output Power
9948.38W
P₂ = P₁ × η
Results are exact for the given inputs using standard gear torque formulas. Actual gear performance depends on tooth profile, material, lubrication, temperature, and operating conditions.
Gear System Diagram
Input Torque
100 N\u00B7m
Output Torque
285.00 N\u00B7m
Output Speed
333.33 RPM
Gear Ratio
3:1
Standard Gear Torque Values
| Ratio | Input T (N\u00B7m) | Output T (N\u00B7m) | Output RPM | Application |
|---|---|---|---|---|
| 0.7:1 | 200 | 133 | 1429 | 6th gear overdrive |
| 1:1 | 200 | 200 | 1000 | Direct drive |
| 3:1 | 200 | 570 | 333 | 1st gear (with 95% eff) |
| 10:1 | 100 | 950 | 100 | Industrial gearbox |
Engineering Data
97-99%
Efficiency per Mesh
i=z\u2082/z\u2081
Ratio Formula
10:1
Max Single Stage
Formula
Output torque equals input torque multiplied by the gear ratio and mesh efficiency. Output speed is inversely proportional to gear ratio. Power is conserved in ideal gears (P_in = P_out), but real gears lose power to friction.
T₂ = T₁ × GR × η
Alternative Form
ω₂ = ω₁ / GR and P = T × ω = 2π × T × RPM / 60
Variables
| Symbol | Name | Unit | Description |
|---|---|---|---|
| T₁ | Input Torque | N·m | Torque applied to the driving gear shaft |
| T₂ | Output Torque | N·m | Torque delivered by the driven gear shaft |
| GR | Gear Ratio | — | Ratio of driven gear teeth to driving gear teeth (N₂/N₁) |
| η | Gear Efficiency | % / 1 | Fraction of power transmitted through the gear mesh |
| ω₁ | Input Angular Velocity | rad/s | Rotational speed of the driving gear |
| ω₂ | Output Angular Velocity | rad/s | Rotational speed of the driven gear |
| P | Power | W | Rate of energy transmission: P = T × ω |
Explanation
Gear ratio multiplies torque but divides speed proportionally. Efficiency reduces the actual output below the ideal value. For example, a 3:1 gear with 95% efficiency produces T₂ = T₁ × 3 × 0.95 = 2.85T₁, not the ideal 3T₁.
Derivation
From power conservation: P_in = P_out/η, so T₁ω₁ = T₂ω₂/η. Since ω₂ = ω₁/GR (speed is inversely proportional to gear ratio), substituting gives T₂ = T₁ × GR × η.
Step-by-Step Calculation
Follow each step to understand how the result is calculated from your inputs.
Step 1
Identify the input torque T₁ and input speed ω₁ (RPM).
T₁ = given, ω₁ = given
T₁:100 N·m
ω₁:1000 RPM
Result: T₁ = 100 N·m at 1000 RPM
Step 2
Determine the gear ratio GR = N₂/N₁.
GR = N₂/N₁
GR:3
Result: GR = 3
Step 3
Identify the gear mesh efficiency η.
η = given (%)
η:95%
Result: η = 95% = 0.9500
Step 4
Calculate the output torque.
T₂ = T₁ × GR × η
T₁:100
GR:3
η:0.9500
Intermediate: T₂ = 100 × 3 × 0.9500 = 285.00
Result: T₂ = 285.00 N·m
Step 5
Calculate the output speed.
ω₂ = ω₁ / GR
ω₁:1000
GR:3
Intermediate: ω₂ = 1000 / 3 = 333.33
Result: ω₂ = 333.33 RPM
Step 6
Calculate input and output power.
P = T × 2π × RPM / 60
T₁:100
RPM:1000
Intermediate: P_in = 100 × 2π × 1000 / 60 = 10471.98 W
Result: P_in = 10471.98 W, P_out = 9948.38 W
Final Answer
285.00
Worked Examples
See how the calculator works with different scenarios.
Scenario
An engine produces 200 N·m at 1000 RPM. The 1st gear ratio is 3.5:1 with 95% transmission efficiency.
Inputs
Input Torque:200 N·m
Input RPM:1000
Gear Ratio:3.5
Efficiency:95%
Calculation
T₂ = 200 × 3.5 × 0.95 = 665 N·m RPM₂ = 1000 / 3.5 = 285.7 RPM
Result
665 N·m output torque at 285.7 RPM
Interpretation
The 3.5:1 reduction nearly triples the torque for strong acceleration. The 5% efficiency loss converts to 35 N·m of lost torque (665 vs. ideal 700 N·m), which appears as heat in the transmission.
Understanding Your Result
Your Result: Output Torque (T₂): 285.00 N·m
Typical range: Spur gears: 98-99% efficiency. Helical gears: 95-98%. Worm gears: 50-90%. Single-stage ratios up to 10:1. Multi-stage compound ratios can exceed 100:1. Automotive transmissions: 0.7:1 to 4.5:1 per gear.
What This Means
The gear torque calculator determines how a gear pair transforms input torque and speed. The fundamental relationship T₂ = T₁ × GR × η shows that output torque is the product of input torque, gear ratio, and mesh efficiency. Speed decreases inversely with the gear ratio.
Why It Matters
Gear torque calculations are essential for sizing gearboxes, selecting motors, designing transmissions, and analyzing drivetrain performance. Incorrect torque estimates can lead to undersized components (failure) or oversized components (wasted cost and space).
Professional Interpretation
In professional practice, gear torque calculations must account for service factors (shock loading), temperature derating, lubrication conditions, and expected gear life. The AGMA rating standards provide systematic methods for determining safe torque capacity based on tooth bending and surface contact stress limits.
Torque multiplication trade-off
Gear systems cannot create power — they trade speed for torque (or vice versa). A 3:1 reduction triples torque but cuts speed to one-third. The product T × ω (power) remains constant in ideal gears and decreases by the efficiency factor in real gears.
Efficiency compounding in multi-stage systems
When gear stages are in series, total efficiency is the product of individual efficiencies. Two stages at 97% give 94.1%, not 94%. Each additional stage compounds losses, which is why high-ratio single-stage gearboxes (like worm gears) are avoided when efficiency matters.
Real-world torque considerations
Nominal gear torque ratings assume steady-state operation. Dynamic effects (starting, stopping, reversing, shock loads) can produce peak torques 2-3x nominal. Design for peak torque with appropriate safety factors, and verify fatigue life at nominal torque.
Recommendations
- •Always include gear efficiency in torque calculations — real gears are never 100% efficient
- •Apply service factors (1.25-2.0) for applications with shock loading or frequent starts/stops
- •Consider thermal capacity: efficiency losses generate heat that must be dissipated
- •For high-ratio applications (>10:1), use multiple stages to maintain reasonable efficiency
- •Select gear type based on application: spur for simplicity, helical for smoothness, worm for self-locking
- •Verify torque capacity against AGMA or ISO standards for the specific gear geometry and material
Typical Value Ranges
| Parameter | Typical Range |
|---|---|
| Design Parameter | Varies by application \u2014 consult reference tables |
| Common Materials | Steel, Stainless Steel, Aluminum, Cast Iron, Brass |
| Design Standard | ASME / ISO / DIN applicable standards |
| Safety Factor Range | 1.5 \u2014 3.0 typical for mechanical design |
| Operating Temperature | -20\u00B0C to 150\u00B0C for standard applications |
| Typical Precision | \u00B12% of calculated value with valid inputs |
Common Applications
| Application | Description |
|---|---|
| General Machinery | Standard industrial equipment and systems |
| Automotive | Vehicle components and powertrain systems |
| Aerospace | Lightweight high-reliability designs |
| Manufacturing | Production equipment and process machinery |
| Energy Sector | Power generation and transmission systems |
Troubleshooting Guide
| Issue | Cause | Solution |
|---|---|---|
| Results seem incorrect | Unit mismatch or input values outside expected range | Verify unit system and check inputs against reference values |
| No results displayed | Empty, zero, or invalid input values | Ensure all required fields have valid positive numbers |
| Unexpected values | Extreme inputs produce results outside practical range | Stay within typical operating parameter ranges |
| Invalid or non-finite | Division by zero or invalid mathematical operation | Check that all inputs are valid positive numbers |
Practical Tips
- •Always include gear efficiency in your calculations — real gears are never 100% efficient
- •For ratios above 10:1, consider multi-stage gearboxes to maintain higher overall efficiency
- •Apply a service factor of 1.25-2.0 for applications with starting loads or shock
- •Remember that torque and speed are inversely related through the gear ratio
- •Check both torque capacity AND speed rating when selecting gears
- •Consider thermal management — efficiency losses generate heat that must be dissipated
- •Use the standard power formula P = T × 2π × RPM / 60 for consistent SI calculations
- •For precision positioning, minimize backlash by using preload or anti-backlash gears
Common Mistakes
Ignoring gear efficiency in torque calculations
Always multiply by efficiency: T_out = T_in × GR × η. Forgetting this overestimates output torque by 2-10%.
Confusing gear ratio direction
GR = N_driven/N_driving. If the output gear has more teeth, GR > 1 and torque increases. If fewer, GR < 1 and speed increases.
Using gear ratio for speed and torque in the same direction
Torque multiplies by GR but speed divides by GR. They move in opposite directions: more torque means less speed, and vice versa.
Not accounting for service factors in dynamic applications
Apply service factors (1.25-2.0) for shock loading, frequent starts, and impact conditions. Nominal torque ratings are for steady-state only.
Selecting gears based only on ratio, not torque capacity
A gear may handle the ratio but fail under the actual torque. Always verify tooth bending stress and surface contact stress against material limits.
Assumptions
This calculator makes the following assumptions to provide estimates:
Rigid Shaft Assumption: The calculation assumes rigid input and output shafts. Shaft deflection under load can alter gear mesh geometry and reduce effective torque transmission.
Steady-State Operation: Torque values are for steady-state conditions. Dynamic effects (acceleration, deceleration, impact) produce transient torques that may exceed calculated values.
Uniform Load Distribution: The calculation assumes torque is uniformly distributed across the gear face width. Misalignment or uneven loading can concentrate stress and reduce effective capacity.
Constant Efficiency: Efficiency is assumed constant across the operating range. In reality, efficiency varies with speed, load, temperature, and lubrication condition.
No Shaft Deflection: The gear geometry is assumed to remain perfect under load. In practice, shaft and housing deflection can alter the gear mesh pattern.
Limitations
Be aware of these limitations when using this calculator:
Thermal Limits Not Modeled: The calculator does not account for thermal capacity. Continuous operation at high torque may exceed the gearbox thermal limit even if torque capacity is adequate.
No Dynamic Analysis: This is a steady-state torque calculation. Dynamic analysis including inertia, acceleration, and torsional vibration is not included.
Gear Strength Not Verified: The calculated output torque is the transmitted torque, not the safe torque capacity. Gear strength must be verified separately using AGMA or ISO standards.
Lubrication Effects Simplified: Efficiency is input as a single value. Real lubrication effects vary with speed, temperature, and oil type and are not modeled in detail.
Frequently Asked Questions
Answers to common questions about this calculator.
What is a Gear Torque Calculator?
The Gear Torque Calculator computes output torque and speed for gear systems using the fundamental gear relationship: T₁ω₁ = T₂ω₂ and the gear ratio N₂/N₁. It is essential for transmission design, gearbox analysis, and drivetrain engineering.
How does gear ratio affect torque?
Gear ratio (GR = N₂/N₁) directly multiplies torque. A reduction gear (GR > 1) increases torque proportional to the ratio while decreasing speed. For example, a 3:1 reduction triples output torque but reduces speed to one-third.
What is the relationship between torque and speed in gears?
Power is conserved (ideal gears): T₁ω₁ = T₂ω₂. Torque and speed are inversely proportional. When torque increases through gear reduction, speed decreases by the same factor, and vice versa.
How do I calculate gear ratio?
Gear ratio = Number of teeth on output gear / Number of teeth on input gear = N₂/N₁. It can also be calculated from pitch diameters: D₂/D₁, or from speeds: ω₁/ω₂.
What is the difference between reduction and overdrive gearing?
Reduction gearing (GR > 1, e.g., 3:1) increases torque and reduces speed, used for acceleration and hill climbing. Overdrive gearing (GR < 1, e.g., 0.7:1) increases speed at the expense of torque, used for highway cruising.
What are typical gear ratio values for automotive transmissions?
Typical ratios: 1st gear 3.5-4.5:1, 2nd 2.0-2.5:1, 3rd 1.3-1.7:1, 4th 1.0:1 (direct), 5th/6th 0.7-0.9:1 (overdrive). Final drive ratio adds another 2.5-4.0:1 multiplication.
How does gear efficiency affect output torque?
Real gears have 90-99% efficiency per mesh. The effective output torque is: T_out = T_in × GR × η. For a 3:1 reduction with 95% efficiency, T_out = T_in × 3 × 0.95 = 2.85 × T_in.
What is torque in gear systems measured in?
Torque is measured in Newton-meters (N·m) in SI units, or pound-feet (lb·ft) and pound-inches (lb·in) in imperial units. The calculator supports all common units with conversion.
How do I calculate power transmitted through gears?
Power P = T × ω = 2π × T × N / 60 (where N is RPM). For consistent units: P (Watts) = T (N·m) × ω (rad/s) = 2π × T × RPM / 60.
What are the different types of gears and their torque characteristics?
Spur gears: simplest, highest efficiency 98-99%. Helical gears: smoother, slightly lower efficiency 95-98%. Bevel gears: change direction, 95-98%. Worm gears: high reduction, lowest efficiency 50-90%.
How does gear material affect torque capacity?
Material choice determines maximum torque capacity. Case-hardened steel gears handle the highest loads. Through-hardened steel, cast iron, and plastic gears have progressively lower capacity. Material selection must consider both strength and wear resistance.
What is the torque capacity of a gear tooth?
Gear tooth torque capacity depends on tooth geometry, material strength, and surface hardness. The Lewis equation and AGMA standards provide methods for calculating tooth bending and pitting resistance for torque capacity.
How do multiple gear stages affect total torque?
Total torque ratio = product of all individual gear ratios. A two-stage gearbox with 3:1 and 4:1 gives 12:1 total reduction, multiplying input torque by 12 (minus efficiency losses).
What is the difference between torque and power in gear systems?
Torque is rotational force (N·m), power is the rate of doing work (Watts). In a lossless gear system, power is constant through the train, but torque and speed change inversely with the gear ratio.
How does gear pitch affect torque transmission?
Larger gear pitch (coarser teeth) increases torque capacity per tooth but may increase noise and vibration. Fine pitch gears are smoother and quieter but have lower individual tooth strength.
What are the AGMA standards for gear torque ratings?
AGMA (American Gear Manufacturers Association) standards 2001-D04 and 2101-D04 provide methods for calculating gear tooth bending and pitting resistance, which determine torque ratings for spur and helical gears.
How does lubrication affect gear torque capacity?
Proper lubrication reduces friction, dissipates heat, and prevents wear. Inadequate lubrication can reduce gear life by 50-90% and significantly lower torque capacity due to increased friction and overheating.
What is the torque-speed product and why is it constant?
The torque-speed product (T × ω) equals power, which remains constant in ideal gear trains (ignoring losses). This is why torque multiplication always comes with proportional speed reduction.
How do I select the right gear ratio for an application?
Determine required output torque and speed, then calculate ratio = ω_in/ω_out = T_out/T_in. Consider efficiency, space constraints, gear type, and number of stages. Multiple stages may be needed for ratios above 10:1.
What is backlash and how does it affect gear torque?
Backlash is the clearance between mating gear teeth. It does not directly affect torque capacity but affects positioning accuracy and can cause impact loading in reversing applications. Minimize backlash for precision systems.
How does temperature affect gear torque transmission?
High temperatures reduce lubricant viscosity, increase wear, and may soften gear materials. For high-temperature applications, use appropriate lubricants and heat-treated steels to maintain torque capacity.
What is the relationship between gear diameter and torque?
For the same tooth load, larger diameter gears transmit proportionally more torque since torque = force × radius. This is why final drive gears in vehicles are larger than input gears.
How are planetary gear systems different for torque?
Planetary gear systems offer higher torque density (torque per unit volume) than parallel shaft gears. A single planetary stage can achieve 3-10:1 ratio with torque distributed across multiple planet gears.
What is torque ripple and how is it managed?
Torque ripple is periodic variation in output torque caused by gear meshing dynamics. It is reduced by using helical gears, increasing contact ratio, and proper gear finishing. High precision gears have minimal ripple.
Can gear torque be measured directly?
Yes, using torque sensors (strain gauge-based) mounted on the gear shafts. Inline torque meters provide real-time torque measurement for both input and output shafts for efficiency calculation.
What is the difference between spur and helical gear torque capacity?
Helical gears have higher torque capacity than spur gears of the same size because multiple teeth are in contact simultaneously (higher contact ratio). They also operate more smoothly with less torque ripple.
How does gear module affect torque transmission?
Larger module (coarser pitch) gears have bigger, stronger teeth that can transmit more torque per tooth. Module selection directly impacts the gear's torque capacity and overall size for a given gear ratio.
What is the efficiency of a worm gear system?
Worm gear efficiency ranges from 50-90%, significantly lower than spur or helical gears (95-99%). The sliding contact between the worm and wheel generates friction losses. Self-locking worm gears (efficiency < 50%) cannot be back-driven.
How do you calculate the tangential force on a gear tooth?
Tangential force F_t = T / r, where T is the torque and r is the pitch radius. This force determines the tooth bending stress and is used in gear strength calculations per AGMA standards.
What is the relationship between face width and torque capacity?
Wider gear faces distribute the load across more tooth area, increasing torque capacity proportionally. However, face width is limited by deflection and load distribution across the tooth. Typical face width is 8-12 times the module.
How does gear helix angle affect torque and efficiency?
Helical gears with larger helix angles have smoother engagement and higher contact ratios, but generate axial thrust that requires thrust bearings. Efficiency drops slightly (95-98% vs 98-99% for spur gears) due to the axial component.
What is the significance of the gear contact ratio for torque?
Contact ratio is the average number of teeth in contact at any time. Higher contact ratio (>1.5) distributes torque load across more teeth, reducing per-tooth stress and enabling smoother torque transmission with less noise.
How do you account for shock loading in gear torque calculations?
Apply a service factor (typically 1.25-2.0) to the nominal torque for shock loading. The service factor accounts for sudden load changes, starting torque, and impact conditions that exceed steady-state torque values.
What is the difference between rated torque and maximum torque?
Rated torque is the continuous torque a gear can transmit without exceeding its design life. Maximum (peak) torque is the highest torque tolerable for short durations without permanent damage. Peak torque can be 1.5-3x rated torque.
How does gear surface finish affect torque transmission efficiency?
Smoother gear surfaces (lower Ra values) reduce friction losses and increase efficiency. Ground and polished gears achieve 98-99% efficiency, while cast or rough-cut gears may only achieve 94-96%. Surface finish also affects noise and wear life.
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Glossary
Technical terms used in mortgage calculations explained in plain language.
- Gear Ratio (GR)
- The ratio of teeth on the driven gear to teeth on the driving gear (N₂/N₁), determining torque multiplication and speed reduction.
- Output Torque (T₂)
- The torque delivered by the driven gear, equal to input torque × gear ratio × efficiency.
- Input Torque (T₁)
- The torque applied to the driving gear (pinion or input shaft).
- Angular Velocity (ω)
- The rate of rotation in radians per second, related to RPM by ω = 2π × RPM / 60.
- Reduction Gearing
- Gear arrangement where output speed is lower and output torque is higher than input (GR > 1).
- Overdrive Gearing
- Gear arrangement where output speed is higher and output torque is lower than input (GR < 1).
- Gear Mesh Efficiency (η)
- The fraction of power transmitted through a gear pair without loss, typically 95-99% for spur/helical gears.
- Spur Gear
- A gear with straight teeth parallel to the axis, the simplest and most efficient gear type.
- Helical Gear
- A gear with angled teeth that engage gradually, providing smoother and quieter operation than spur gears.
- Planetary Gear
- A gear system with sun, planet, and ring gears offering high torque density in a compact package.
- Worm Gear
- A gear set with a screw-like worm driving a wheel, providing high reduction ratios (10:1 to 100:1) in a single stage.
- Contact Ratio
- The average number of teeth in mesh at any time; higher values mean smoother torque transmission.
- Backlash
- The clearance between mating gear teeth, affecting positioning accuracy and impact loading.
- Module
- The ratio of pitch diameter to number of teeth, determining tooth size and gear strength.
- Pitch Circle
- The theoretical circle on which gear calculations are based, where the gear ratio is defined.
- Service Factor
- A multiplier applied to nominal torque to account for shock loading, duty cycle, and reliability requirements.
- AGMA
- American Gear Manufacturers Association — publishes gear design and rating standards.
- Tooth Bending Stress
- The stress in the gear tooth root due to tangential force, calculated using the Lewis or AGMA equations.
- Pitting
- Surface fatigue failure of gear teeth caused by repeated contact stress exceeding the material endurance limit.
Authoritative References
Trusted sources and standards referenced by this calculator.
AGMA — Gear Rating Standards Engineering Toolbox — Gears MIT OCW — Machine Design Norton — Machine Design RoyMech — Gears Reference KHK Gears Technical Reference ASME — Power Transmission Machine Design Magazine
Applicable Standards
AGMA 2001-D04 — Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear TeethAGMA 2101-D04 — Metric Edition of AGMA 2001-D04ISO 6336 — Calculation of load capacity of spur and helical gearsDIN 3990 — Calculation of load capacity of spur and helical gearsANSI/AGMA 6013 — Standard for Industrial Enclosed Drives
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Last Updated:
2026-08-21
Version:
2.0.0
References:
License:
Free to use for educational and professional purposes.