Rolling Resistance Calculator

Estimate steady rolling-resistance force, equivalent moment, power loss, and energy per distance from a coefficient or force-offset length.

Engineering screening tool—verify inputs and results independently. Use at your own risk.

Load, contact, and speed

Load definitionMass mode calculates N = mg; direct mode uses the entered compressive load.
Supported mass, mTotal mass carried by the modeled rolling contacts.
Gravity, gm/s²Positive local acceleration; used only in mass mode.

Resistance definitionThe two definitions are connected by Crr = b/r.
Coefficient, Crr—Positive force ratio; no material presets are assumed.

Effective rolling radius, rPositive effective radius, up to 100 m equivalent.
Travel speed, vNon-negative steady speed, up to 200 m/s equivalent.
Force display unitChanges the canonical force display only.

Rolling-resistance result

Rolling-resistance force—N

Normal load— N

Equivalent coefficient—

Resistance length— mm

Power loss—

Resistance moment— N·m

Energy per distance— J/m

Power versus speed

Equations used

N = mg (mass mode, level ground)

F_rr = C_rrN

M_rr = F_rrr = Nb

C_rr = b/r

P_rr = F_rrv

E/s = F_rr

Symbols and units: N is positive compressive normal load (N), m is supported mass (kg), g is gravity (m/s²), F_rr is the non-negative rolling-resistance magnitude (N), C_rr is dimensionless, b is the equivalent normal-force offset (m), r is effective rolling radius (m), M_rr is resisting moment (N·m), v is speed (m/s), P_rr is power (W), and E/s is energy per distance (J/m). The physical force acts opposite travel; the page reports its magnitude.

Assumptions and limits

This is a level-ground, steady, rigid-wheel equivalent model with constant load, coefficient, radius, and speed. It combines all contacts into one force. It does not derive coefficients from material names and omits grade, aerodynamic drag, bearing/seal drag, tyre pressure and speed effects, temperature, deformation transients, sinkage, lubrication, acceleration, and slip. It is unsuitable for braking or traction limits, bearing life, soft-terrain mobility, or safety qualification.

References

ISO 28580:2018, tyre rolling-resistance single-point measurement and correlation (method context; this page does not reproduce its test procedure).
Engineering Mechanics — Rolling Resistance, statics moment-balance treatment.
Rolling Resistance calculator, functional field-set reference.

How to use

Select Supported mass to calculate N = mg on level ground, or Direct normal load when the carried compressive load is already known.
Enter the required load value and its unit. In mass mode, enter local gravity in m/s².
Select Dimensionless coefficient to enter C_rr, or Equivalent resistance length to enter b. Do not infer either value from an unrelated material preset.
Enter effective rolling radius and its unit. The calculator requires 0 < C_rr = b/r ≤ 0.5.
Enter non-negative travel speed and choose a force display unit.
Select Calculate to update force, load, coefficient, length, moment, power, energy per distance, and the power plot. Correct any red warning before using results.
Interpret F_rr as a steady opposing-force magnitude. Power varies linearly with speed under the constant-coefficient assumption; zero speed gives zero power but retains the force estimate.
Select Reset example to restore the documented demonstration. Do not use this model when grade, slip, soft-ground sinkage, thermal effects, or detailed bearing/tyre behavior controls the result.

Worked example

1. Choose mass and coefficient modes. 2. Enter m = 1000 kg, g = 9.80665 m/s², C_rr = 0.015, r = 300 mm, and v = 10 m/s. 3. Calculate. The expected normal load is 9806.65 N, rolling resistance is 147.10 N, equivalent b is 4.5 mm, moment is 44.13 N·m, and power is 1.471 kW. This means about 1.47 kW is required solely for the modeled rolling resistance at that speed; other losses remain separate.

Theory and method

A deforming rolling contact can be represented statically by shifting the normal-force resultant forward by b. Moment balance about the wheel center gives F_rrr = Nb; dividing by Nr gives C_rr = F_rr/N = b/r. The calculator accepts either equivalent parameter and reports the other. Multiplication by steady speed converts opposing force to mechanical power. Real coefficients are empirical operating-point quantities and should come from relevant measurements or a traceable specification.

Continue in TriboSolver

Use TriboSolver to refine contact loads, materials, lubrication, thermal behavior, and speed-dependent losses when the constant-coefficient screen is insufficient.