Rolling-Bearing Geometry, Fits, and Operating Clearance Calculator

Bearing and installation inputs

Results update automatically. Enter internal geometry and explicit fit deviations rather than a bearing designation.

Geometry result

Signed values distinguish residual clearance from preload.

Result

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Equations used

All dimensions and signed clearances are diametral millimetre values. Positive clearance means separation; negative clearance means calculated preload. Temperature differences in °C and K are numerically identical.

d_m = (d_i + d_o)/2

P_d = d_o − d_i − 2D

A = (f_i + f_o − 1)D

cos α = 1 − P_d/(2A); P_e = 2A sin α

θ = 2 cos⁻¹{1 − [P_d/(4d_m)](q_i + q_o)}, where q_i = [(2f_i−1)D−P_d/4]/[d_m+(2f_i−1)D−P_d/2] and q_o = [(2f_o−1)D−P_d/4]/[d_m−(2f_o−1)D+P_d/2]

cos β = cos α[1 − S_d/(2r_o)]; P_e = 2r_o(sin β − sin α) + S_d sin α

I_eff = δ_mating − δ_bearing − s; Δd_race = max(0, I_eff)η

P_dm = P_d − Δd_i − Δd_o

ΔP_th = α_od_oΔT_o − α_id_iΔT_i − 2α_eDΔT_e

P_do = P_dm + ΔP_th

α_op = atan2[A sin α₀, A cos α₀ − ΔP_d/2]

Symbols: d_m is pitch diameter; d_i and d_o are inner- and outer-raceway diameters; D is rolling-element diameter; P_d, P_dm, and P_do are free, mounted, and operating diametral clearance; f_i and f_o are groove-conformity ratios; A is groove-center distance; α, α₀, and α_op are unloaded contact angles; P_e is axial endplay; δ is a signed dimensional deviation; s is surface-finish allowance; η is a 0–1 raceway transfer ratio; Δd_i and Δd_o are fit-induced raceway changes; α_i, α_o, and α_e are linear thermal-expansion coefficients in 1/K; ΔT is component temperature rise; θ is free ball-bearing misalignment angle; β is the spherical-roller displaced angle; r_o is outer-raceway contour radius; and S_d is spherical-roller diametral clearance.

Assumptions and limits

Use measured internal geometry or current manufacturer data; the calculator does not infer geometry or clearance from a designation.
Fit transfer ratios must come from a validated elastic ring/shaft/housing model, measurement, or supplier guidance.
Uniform component temperatures and linear thermal expansion are assumed. Load deformation, ring ovalization, loaded/allowable misalignment, and speed effects are excluded.
The reported ball-bearing misalignment is an unloaded geometric free angle, not an allowable operating limit.
Negative operating clearance indicates calculated preload and requires a complete bearing-system suitability check.

How to use

Select Ball geometry, Cylindrical roller, Spherical roller, Fits and mounted clearance, or Operating clearance.
For ball geometry, enter measured raceway and ball dimensions in millimetres plus both groove-conformity ratios; read clearance, contact angle, endplay, and geometric free misalignment.
For cylindrical rollers, enter roller and raceway diameters in millimetres. For spherical rollers, enter outer contour radius, nominal contact angle, and free diametral clearance.
For fits, enter explicit signed shaft, bearing, and housing deviations in millimetres, the finish allowance, and validated transfer ratios from 0 to 1.
For operating clearance, enter free clearance, fit-induced raceway changes, the initial angle and groove-center distance, then each component diameter, expansion coefficient in µm/m·K, and temperature rise in °C.
Calculate by editing any field; results update automatically. Use Reset example to restore all examples and return to Ball geometry.
Read positive clearance as separation and negative clearance as calculated preload. Review any warning before using the result in a bearing selection.
This model should not be used for loaded contact deformation, ring ovalization, allowable operating misalignment, centrifugal effects, fatigue life, or catalog suitability decisions.

Reference

Harris, T. A. and Kotzalas, M. N. (2006), Advanced Concepts of Bearing Technology: Rolling Bearing Analysis, Fifth Edition, CRC Press, Volume I, Chapters 2–3. doi:10.1201/9781420006582.