August 2026 14 min read

Journal Bearing Calculator

Free journal bearing calculator using Raimondi–Boyd hydrodynamic theory. Compute the Sommerfeld number, eccentricity, minimum film thickness, friction coefficient, torque, power loss and oil flow for your sleeve bearing.

Journal Bearing Calculator

Journal Bearing Inputs

Journal Diameter d (m)

Shaft diameter (e.g. 0.05 = 50 mm)

Bearing Length L (m)

Axial length of the sleeve

Radial Clearance c (m)

Gap = (bearing radius − journal radius); 1e-4 = 0.1 mm

Speed n (rpm)

rpm

Shaft rotational speed

Load W (N)

Radial bearing reaction

Viscosity μ (Pa·s)

Pa·s

Absolute viscosity at operating temperature (0.01–0.1 typical)

Oil Density ρ (kg/m³)

kg/m³

For flow temperature-rise estimate

Oil Specific Heat c_p (J/kg·K)

J/kg·K

≈ 1900 for mineral oil

Auto-calculate instantly

Minimum Film Thickness h_min

0.0010mm

At ε = 0.99. Keep above the roughness + margin to avoid contact.

Film too thin — risk of contact / seizure

Sommerfeld No. S

0.01172

Eccentricity ε

0.99

Friction coeff. f

0.00000

Friction Torque

8.66e-8N·m

Power Loss

1.63e-8kW

Oil Flow Q

4.215cm³/s

Attitude φ

3.9°

Proj. Press. P

3.2MPa

Sommerfeld No. S

0.01172

Dimensionless film parameter

Eccentricity ε

0.99

e / c

Friction coeff. f

0.00000

Friction / load

Friction Torque

8.66e-8N·m

f·W·r

Power Loss

1.63e-8kW

Heat in the film

Oil Flow Q

4.215cm³/s

Side leakage

Attitude φ

3.9°

Load vs line of centres

Proj. Press. P

3.2MPa

W / (d·L)

Result Summary

Journal Diameter	50 mm
Length	50 mm (L/D 1)
Radial Clearance	0.100 mm
Speed	1,800 rpm
Load W	8,000 N
Viscosity μ	0.02 Pa·s
Sommerfeld S	0.01172
Eccentricity ε	0.99
h_min	0.0010 mm
Power Loss	1.63e-8 kW

Estimated Result — Uses the classic Raimondi–Boyd L/D = 1 solution: the Sommerfeld number is computed exactly from geometry and operating conditions, then ε, h0/c, (r/c)f, Q/(rcN) and φ are interpolated from the published tables. Results are accurate to a few percent for an ungrooved L/D = 1 bearing. For L/D ≠ 1, grooves, or thermal effects, apply the fuller thermo-hydrodynamic analysis. Viscosity should be taken at the bearing's operating temperature.

Interactive Diagram

The shaft sits eccentrically inside the shell; the thinnest gap (bottom, opposite the load line by φ) is the minimum film thickness h_min that governs safe operation.

Visualizations

Key Journal Bearing Quantities

1scaledS (×100)

99scaledε (×100)

0scaledf (×1000)

1scaledh_min (µm)

0scaledP loss (W)

42scaledQ (cm³/s×10)

Film Safety (h_min above roughness)

h_min1µm

Formula

The Sommerfeld number S is the single parameter that determines the entire hydrodynamic state of a journal bearing. Once S is known (here via the L/D = 1 Raimondi–Boyd tables), the eccentricity ratio ε, minimum film thickness, friction coefficient, flow and attitude angle follow. The friction torque is then the lubricant drag times the journal radius, and the power loss is that torque times angular speed — the heat the oil must remove.

S = (r/c)² · μ · N / P

Alternative Form

h_min = c·(1 − ε) | f = [(r/c)·f · S] / (r/c)² | T = f·W·r | Power = T·ω

Variables

Symbol	Name	Unit	Description
S	Sommerfeld number	—	(r/c)²·μ·N/P
r	Journal radius	m	d/2
c	Radial clearance	m	Bearing radius − journal radius
μ	Absolute viscosity	Pa·s	At operating temperature
N	Speed	rev/s	n/60
P	Projected pressure	Pa	W/(d·L)
ε	Eccentricity ratio	—	e/c, from chart
h_min	Minimum film thickness	m	c·(1−ε)
f	Friction coefficient	—	From chart
W	Load	N	Bearing reaction
Q	Oil flow	m³/s	Side leakage

Explanation

A journal bearing is a wedge that generates its own pressure: as the shaft rotates, it drags oil into a converging gap, building a pressure film that lifts the load. The Sommerfeld number tells you how "stiff" that wedge is — high S (fast, light, viscous, tight) means the shaft floats nearly centred with a thick film; low S (slow, heavy, thin, loose) means it rides close to the shell with a thin, risky film. The design art is choosing geometry and oil so ε sits in the safe 0.6–0.9 band with h_min well above the surface roughness.

Derivation

From the Reynolds equation for a long bearing, the steady-state solution is parameterised by S = (r/c)²·μ·N/P. Raimondi and Boyd solved this numerically and published ε, h0/c, (r/c)f and Q/(rcN) as functions of S for various L/D. We use their L/D = 1 set. The friction relation f = [(r/c)f·S]/(r/c)² and h_min = c·(1−ε) close the design equations; torque and power follow from T = f·W·r and Power = T·ω.

Step-by-Step Calculation

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

Step 1

Compute the radius, clearance ratio and speed in rev/s.

r = d/2, r/c = r/c, N = n/60

d:50 mm

c:0.100 mm

n:1,800 rpm

Intermediate: r = 0.025 m, r/c = 250, N = 30 rev/s

Result: Geometry and speed established

Step 2

Form the projected pressure P = W / (d·L).

P = W / (d·L)

W:8,000 N

d·L:2.50e-3 m²

Intermediate: P = 3.2 MPa

Result: Load intensity found

Step 3

Compute the Sommerfeld number.

S = (r/c)² · μ · N / P

(r/c)²:62,500

μ:0.02 Pa·s

N:30

P:3,200,000 Pa

Intermediate: S = 62,500 × 0.02 × 30 / 3,200,000

Result: S = 0.01172

Step 4

Invert the Raimondi–Boyd L/D = 1 table for ε, h0/c, (r/c)f, Q/(rcN) and φ.

ε, h0/c, (r/c)f, Q/(rcN), φ = f(S) [interpolated]

S:0.01172

Intermediate: Interpolating the chart at S = 0.01172

Result: ε = 0.99, h0/c = 0.01, (r/c)f = 2.31e-3

Step 5

Find minimum film thickness and friction coefficient.

h_min = c·(1−ε), f = [(r/c)f · S] / (r/c)²

c:1.00e-4 m

ε:0.99

(r/c)f:2.31e-3

Intermediate: h_min = 1.00e-4 × (1 − 0.99)

Result: h_min = 0.0010 mm, f = 0.00000

Step 6

Compute torque, power and flow.

T = f·W·r, Power = T·ω, Q = (Q/rcN)·r·c·N

f:4.33e-10

W:8,000 N

r:0.025

ω:188.5

Intermediate: T = 8.66e-8 N·m, Q = 4.215 cm³/s

Result: Power loss = 1.63e-8 kW

Final Answer

0.0010 mm

Worked Examples

See how the calculator works with different scenarios.

Scenario

A 50 mm, lightly loaded, moderate-speed journal bearing in SAE oil.

Inputs

d:50 mm

L:50 mm

c:0.1 mm

n:1800 rpm

W:8000 N

μ:0.02 Pa·s

Calculation

P = 8000/(0.05·0.05) = 3.2 MPa; r/c = 250; S = 250²·0.02·30/3.2e6 = 0.117; from chart ε ≈ 0.73, f ≈ 0.0072

Result

h_min ≈ 0.027 mm, power loss ≈ 0.85 kW

Interpretation

A healthy moderate-ε film — typical of a well-designed lightly loaded bearing.

Understanding Your Result

Your Result: 0.0010 mm

Typical range: Sommerfeld numbers for practical bearings span roughly 0.03 (heavy, slow) to 1+ (light, fast). Your S = 0.01172 and h_min = 0.0010 mm fall in the risky range.

What This Means

For a 50 mm journal at 1,800 rpm under 8,000 N, the Sommerfeld number is 0.01172 giving ε = 0.99 and a minimum film thickness of 0.0010 mm. The friction coefficient is 0.00000 and the film dissipates 1.63e-8 kW.

Why It Matters

Journal bearings run for decades in turbines, pumps and engines precisely because the oil film avoids wear. But the film is thin — often tens of microns — so a wrong clearance, viscosity or load can collapse it and seize the shaft. This calculator turns those choices into the single number that matters (h_min) so you can design for a safe, cool, long-lived film.

Professional Interpretation

Aim for ε between 0.6 and 0.9 and h_min several times the combined roughness (Ra₁+Ra₂). If h_min is low, raise viscosity or r/c, or reduce load/speed. Iterate with the heat balance since μ depends on the temperature the power loss creates.

Sommerfeld number

S = 0.01172 — ε near 1, very thin film, heavy/slow duty.

Eccentricity & film

ε = 0.99, h_min = 0.0010 mm, attitude φ = 3.9°.

Losses

f = 0.00000, torque = 8.66e-8 N·m, power = 1.63e-8 kW, flow = 4.215 cm³/s.

Recommendations

•Keep h_min above the combined surface roughness plus a safety margin (≈ 2–3× Ra₁+Ra₂).
•Your h_min is thin — increase viscosity, r/c, or reduce the load to lift ε into the safe band.
•Use viscosity at the operating temperature, not the catalogue room-temperature value.
•Ensure enough oil flow to carry away the computed power loss as heat.
•For L/D ≠ 1, apply a correction or full thermo-hydrodynamic analysis.

Educational Content

Introduction

Unlike a ball bearing, a journal bearing has no rolling parts — a shaft simply spins inside a lubricated sleeve. The genius of the design is that rotation itself pumps oil into a wedge that lifts the entire load off the metal. The journal bearing calculator quantifies that wedge: from your diameters, clearance, speed, load and oil viscosity it predicts the Sommerfeld number, how far the shaft sits off-centre, and how thick the all-important oil film is.

Concept Explanation

The Reynolds equation of lubrication shows that a journal bearing's steady state depends on one dimensionless group, the Sommerfeld number S = (r/c)²·μ·N/P. Larger S (fast, light, viscous, tight clearance) means the shaft floats nearly centred with a thick, safe film; smaller S (slow, heavy, thin oil, loose) means the shaft rides close to the shell with a thin, risky film. Raimondi and Boyd solved the equation numerically and published how ε (eccentricity), h_min/c, friction and flow vary with S for each L/D. This tool uses their L/D = 1 tables, interpolating for your exact S.

Applications

▸Sizing sleeves for turbines, pumps, compressors and gearboxes

▸Selecting clearance and oil viscosity for a given load and speed

▸Checking film safety against surface roughness

▸Estimating friction power loss and the required oil flow

▸Diagnosing hot or noisy bearings (thin-film conditions)

▸Teaching hydrodynamic lubrication and the Sommerfeld number

Benefits

•Gives the real hydrodynamic film thickness, not a guess
•Built on the standard Raimondi–Boyd L/D = 1 solution
•Reports friction, torque, power loss and flow together
•Flags seizure risk when h_min drops too low
•SI consistent and instant

Limitations

•L/D fixed at 1 — not valid for short/long bearings without correction
•Assumes isothermal, steady, fully flooded conditions
•No grooves, misalignment or thermal deformation
•Uses separate viscosity — the heat balance is not closed automatically
•Surface roughness / boundary lubrication not modelled

Best Practices

•Enter viscosity at the expected operating temperature
•Target ε ≈ 0.6–0.9 with h_min comfortably above roughness
•Confirm oil flow can carry away the computed power loss
•Iterate: power loss raises temperature, which lowers μ, which changes S
•For L/D far from 1, use a corrected chart or full analysis

Common Misconceptions

Myth: More clearance is always safer.

Truth: Too much clearance lowers r/c, weakens the film and raises leakage; there is an optimum band (~0.1–0.2% of diameter).

Myth: Friction rises with load here.

Truth: Within the hydrodynamic regime higher load raises ε and can lower the friction coefficient f, even though total torque still rises with load.

Myth: Any oil viscosity works.

Truth: Viscosity sets S; too thin → film collapse and seizure, too thick → excessive power loss and heat.

Myth: The film is thick and robust.

Truth: h_min is often only tens of microns — smaller than a human hair — so contamination and roughness matter enormously.

Practical Tips

•h_min ≈ 0.0010 mm — keep it above roughly 2–3× your combined surface roughness.
•If h_min is small, raise oil viscosity or r/c, or lower the load/speed — but watch the resulting power loss.
•Use viscosity measured at the bearing's running temperature, not the cold oil value.
•Make sure the supply flow exceeds Q so the film stays cool.
•L/D = 1 was assumed; for very short or long bearings, correct the chart coefficients.

Common Mistakes

Using room-temperature viscosity

Enter μ at the operating temperature — oil thins with heat and S changes strongly.

Ignoring the L/D assumption

These coefficients are for L/D = 1; other ratios need a corrected chart.

Treating h_min as large

It is tens of microns; compare to Ra and keep a margin or contact occurs.

Forgetting the heat loop

Power loss heats the oil, lowering μ and S — iterate the temperature.

Wrong clearance units

Use the radial clearance c (not diametral) in metres; a factor-of-2 error flips the result.

Assumptions

This calculator makes the following assumptions to provide estimates:

L/D = 1: Raimondi–Boyd coefficients are for length/diameter = 1.

Steady, isothermal: Constant speed, load and temperature; no thermal coupling.

Fully flooded: Adequate oil supply; no starvation or grooves.

Incompressible Newtonian oil: Standard lubricant behaviour, constant μ.

Limitations

Be aware of these limitations when using this calculator:

L/D fixed: Only the L/D = 1 chart is used; other ratios need correction.

No thermal feedback: Viscosity is an input, so the heat balance is not closed.

No roughness model: Boundary/partial lubrication at start-up is outside this hydrodynamic solution.

Single bearing: No shaft flexibility, misalignment or multi-bearing interactions.

Frequently Asked Questions

Answers to common questions about this calculator.

What is a journal bearing?

A journal bearing supports a rotating shaft with a full or partial sleeve of lubricant instead of rolling elements. A thin hydrodynamic film carries the load, so there is no metal-to-metal contact once running speed is reached.

What does a journal bearing calculator give?

Given shaft diameter, clearance, speed, viscosity, length and load, it returns the Sommerfeld number, eccentricity ratio, minimum film thickness, coefficient of friction, friction torque, power loss and lubricant flow.

What is the Sommerfeld number?

S = (r/c)² · μ · N / P, a dimensionless grouping that collapses speed, load, viscosity, radius and clearance into one parameter controlling the film. It is the master variable of hydrodynamic bearing design.

What is the eccentricity ratio ε?

ε = e / c is how far the shaft centre is displaced from the bearing centre, divided by the radial clearance. ε = 0 is centred (no load), ε → 1 means the shaft nearly touches the bearing (very thin film).

Why must the minimum film thickness stay above zero?

h_min = c·(1 − ε) is the thinnest part of the oil film. If it drops below the combined surface roughness plus a safety margin, asperities touch, friction spikes and the bearing seizes. Design rules keep h_min well clear of the roughness.

What is the r/c ratio?

The radius-to-clearance ratio, typically 500–2000 for machinery. A smaller clearance (large r/c) gives a stiffer, higher-pressure film but is less forgiving of misalignment and dirt.

How is friction coefficient found?

From Raimondi–Boyd charts: f·(r/c) / S is a function of ε (and L/D). We interpolate the L/D = 1 table to get (r/c)·f, then divide by r/c to obtain f.

What is the friction torque?

T = f · W · r, where W is the load on the bearing and r the journal radius. It is the moment the lubricant drag applies to the shaft.

Where does the power loss come from?

P_loss = 2π · n · T, i.e. torque times angular speed. It appears as heat that the oil must carry away or the bearing overheats.

What is the flow Q?

The volumetric side leakage of lubricant, Q ≈ (Q/rcN)·r·c·N from the chart. It both cools the film and, in pressure-fed bearings, supplies the needed oil.

What is the L/D ratio?

Bearing length divided by diameter. Long bearings (L/D ≈ 1) carry more load and leak less but run hotter; short bearings (L/D < 0.5) are cooler and tolerate misalignment. This tool uses the L/D = 1 chart.

What is the attitude angle φ?

The angle between the load line and the line of centres. It tells you where the minimum film sits relative to the load — important for feeding oil into the converging (thick-film) side.

Why is the L/D = 1 assumption important?

Raimondi–Boyd chart coefficients depend strongly on L/D. Using L/D = 1 is the textbook standard; for a different L/D the coefficients shift, so treat non-1 results as approximate.

What viscosity should I use?

Use the operating temperature viscosity of the oil, not the room-temperature value. Oil thins with heat, so the right μ is the one at the bearing's steady running temperature (often found by iteration with the heat balance).

What is boundary vs hydrodynamic lubrication?

Below a critical speed the film cannot form (boundary lubrication) and surfaces touch — high wear. Above it, the wedge action builds a full film (hydrodynamic) and the bearing runs with near-zero wear.

How do I avoid seizure?

Keep h_min above the roughness + margin, control inlet temperature, ensure enough flow, and never overload past the ε → 1 region where the film collapses.

What is a clearance fit?

The manufactured gap between journal and bearing. Diametral clearance = 2c; typical values are 0.1–0.2% of the diameter. Too tight risks contact, too loose wastes flow and stability.

What is the minimum speed for a full film?

There is a threshold where μ·N/P becomes large enough that ε drops below ~0.8 and a safe film forms. Below that, start-up and stop are in boundary lubrication and need a thin-film or boundary additive.

How is journal bearing different from a ball bearing?

A journal bearing has no rolling elements — just a shaft in a lubricated sleeve. It handles heavier, slower, dirtier loads quietly but needs a reliable oil supply and good alignment.

What is the friction variable?

The coefficient f is dimensionless (friction force / load). In journal bearings f is typically 0.001–0.01 once the film is established — far lower than dry contact.

Can I size a bearing from this?

Yes, as a first estimate: pick diameter, L/D, clearance and oil so that ε lands in the 0.6–0.9 sweet spot with h_min above roughness. Final design needs a full thermo-hydrodynamic check.

What is the heat balance?

Power loss = heat in; oil flow × specific heat × temperature rise = heat out. Matching them sets the operating temperature, which sets μ, which sets ε — a loop you may iterate.

What is the Ocvirk number?

The short-bearing approximation where L/D is small; it simplifies the Sommerfeld solution. Long-bearing (this chart) and short-bearing results bracket real designs.

Why does f fall as load rises here?

Counter-intuitively, raising load raises ε, which raises (r/c)f only mildly while S falls fast; the net coefficient f can drop at high load because the high film pressure does the load sharing. The chart captures this.

What is the maximum load capacity?

It corresponds to ε → 1 (h_min → 0). Practical capacity is set by the ε where h_min hits the roughness limit, not the theoretical max.

How does temperature rise relate to flow?

ΔT ≈ Power_loss / (ρ · Q · c_p). More flow lowers the temperature rise; too little flow lets the oil overheat and thin out, risking collapse.

What oil properties matter?

Absolute viscosity μ (Pa·s), density ρ (kg/m³) and specific heat c_p (≈ 1900 J/kg·K for oil). Viscosity dominates the Sommerfeld number.

Is the result exact?

It is the classic Raimondi–Boyd L/D = 1 solution, accurate to a few percent for that geometry. Real bearings with L/D ≠ 1, grooves or thermal effects need the fuller analysis.

What about grooving?

Oil grooves interrupt the film and change the effective L/D; a circumferential groove at the unloaded side is common. This tool assumes an ungrooved L/D = 1 film.

How do I read the chart values?

This calculator interpolates the published tables for ε, h0/c, (r/c)f, Q/(rcN) and φ directly from the Sommerfeld number, so you get the numbers without reading plots by eye.

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Related Guides

Deepen your understanding with these educational resources.

Raimondi & Boyd — Design of journal bearings (ASME)

The original tabulated solution used here.

SKF — Hydrodynamic journal bearings

Manufacturer design guidance.

MIT OCW — Lubrication

University material on fluid-film lubrication.

Glossary

Technical terms used in mortgage calculations explained in plain language.

Journal: The rotating shaft portion that runs inside the bearing.
Sommerfeld Number (S): Dimensionless (r/c)²·μ·N/P governing the film; the master bearing parameter.
Eccentricity Ratio (ε): e/c — shaft-offset over clearance; 0 centred, →1 near contact.
Minimum Film Thickness (h_min): c·(1 − ε); thinnest oil gap, must exceed roughness.
Radial Clearance (c): Bearing radius minus journal radius; diametral = 2c.
r/c Ratio: Radius-to-clearance ratio, typically 500–2000.
Coefficient of Friction (f): Friction force divided by the bearing load.
Attitude Angle (φ): Angle between load line and line of centres.
L/D Ratio: Bearing length over diameter; sets chart coefficients.
Friction Torque (T): f·W·r — drag moment on the shaft.
Power Loss: 2π·n·T — heat generated in the film.
Flow (Q): Side-leakage volumetric oil flow.

Authoritative References

Trusted sources and standards referenced by this calculator.

Raimondi & Boyd — Journal Bearing Charts (ASME) Cameron — Basic Lubrication Theory Shigley's Mechanical Engineering Design — Bearings Hamrock — Fundamentals of Fluid Film Lubrication SKF — Hydrodynamic journal bearings MIT OpenCourseWare — Lubrication

Applicable Standards

Raimondi–Boyd (L/D = 1)ASME design chartsISO 7902 (hydrodynamic bearings)Shigley design practice

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Last Updated:

August 2026

Version:

2.1.0

References:

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Free to use for educational and professional purposes.