Rolling Resistance Coefficient Calculator

This calculator estimates the rolling resistance coefficient (Crr) from the force needed to keep a wheel rolling at constant speed, the load on the wheel, and the wheel radius. Enter the measured force, the vertical load, and the radius, and you get the dimensionless Crr value plus the rolling resistance force. The result is the standard ratio used in vehicle dynamics, tire testing, and efficiency calculations.

Formula

The rolling resistance coefficient is defined as the ratio of the force required to overcome rolling resistance to the normal load on the wheel:

Crr = F / N

• F – horizontal force needed to keep the wheel rolling at constant speed (newtons, N)
• N – vertical load on the wheel (newtons, N)
• Crr – dimensionless coefficient (unitless)

Note: The wheel radius is not part of the basic Crr formula, but it is included here because many real measurements give torque rather than force. If you have torque (T) and radius (r), the force is F = T / r. This calculator accepts force directly, but you can compute force from torque by dividing by the radius.

Worked Example

Using the default values from the calculator:

1. Force (F) = 10 N
2. Load (N) = 100 N
3. Radius (r) = 0.3 m

Crr = F / N = 10 / 100 = 0.100

The rolling resistance force is simply the input force, 10 N. The coefficient 0.100 is high for a typical tire (most car tires are 0.01–0.015), but the defaults are chosen for easy arithmetic. For a real measurement, you would use your actual force and load values.

How Rolling Resistance Coefficient Is Measured

The most common lab method is the drum test: a wheel is pressed against a rotating drum, and the force needed to keep the drum turning at constant speed is measured. That force divided by the load gives Crr. Field methods use a towed trailer with a load cell, or a coast-down test where deceleration is measured and Crr is extracted from the equation of motion. In all cases, the key is that the wheel is rolling freely (no drive torque) and speed is constant, so the measured horizontal force equals the rolling resistance.

Typical Values for Common Surfaces

Rolling resistance coefficient varies widely with surface and tire type. These are approximate ranges for a loaded wheel at moderate speed:

• Rail steel wheel on steel rail: 0.001 – 0.002
• Bicycle tire on smooth asphalt: 0.004 – 0.008
• Car tire on concrete: 0.010 – 0.015
• Car tire on gravel: 0.020 – 0.030
• Car tire on sand: 0.15 – 0.30

These values are for reference only; your actual measurement may differ due to tire pressure, temperature, tread design, and speed.

How to Use the Result

The Crr value is used in the rolling resistance force equation:

F_rr = Crr × N

Where N is the normal load (weight on that wheel). For a vehicle, multiply by the total weight to get total rolling resistance. This force is then used in power calculations: Power = F_rr × speed. For example, a 1000 kg car (load ≈ 9810 N) with Crr = 0.012 has rolling resistance of about 118 N. At 30 m/s (108 km/h), that requires about 3.5 kW just to overcome rolling resistance, before air drag.

Common Mistakes and How to Avoid Them

• Using mass instead of weight: The load N must be in newtons. If you have mass in kg, multiply by 9.81 m/s² to get newtons.
• Mixing units: Force must be in newtons, not pounds or kgf. Convert lbf to N (1 lbf ≈ 4.448 N) and kgf to N (1 kgf ≈ 9.81 N).
• Measuring at the wrong speed: Crr is speed-dependent, though mildly. Measure at the speed you care about, or note the speed when reporting.
• Not accounting for bearing friction: In a drum test, the measured force includes bearing losses. Subtract bearing friction measured separately, or use a low-friction bearing.
• Confusing Crr with friction coefficient: Rolling resistance is about deformation, not sliding friction. Crr is typically 10–100 times smaller than the static friction coefficient.

Limitations of the Simple Formula

The basic Crr = F/N formula assumes a linear relationship between load and resistance, which holds well for most tires at normal loads but fails at very high or very low inflation pressures. It also ignores speed effects, temperature, and the fact that Crr can change with load on soft surfaces. For precise engineering work, you would use a more complex model, but the simple coefficient is adequate for most comparisons and estimates.

Frequently Asked Questions

What is a good rolling resistance coefficient for a car tire?

For a modern passenger car tire on asphalt, a Crr between 0.010 and 0.015 is typical. Low-rolling-resistance tires (often labeled as such) may achieve 0.008–0.010. Values below 0.008 are rare for road tires but common for bicycle tires.

How does tire pressure affect Crr?

Higher inflation pressure reduces tire deformation, which generally lowers Crr. However, over-inflation can reduce grip and ride comfort. The relationship is not linear, and the optimal pressure depends on the load and speed.

Can I calculate Crr from a coast-down test?

Yes. Measure the deceleration of a freely rolling vehicle at a known speed. The deceleration a is related to Crr by a = Crr × g (plus aerodynamic drag, which must be subtracted). This method requires accurate speed data and a calm day to separate rolling resistance from air drag.

Does Crr change with speed?

Yes, but mildly for most tires. At very low speeds, Crr is roughly constant; above about 50 km/h it may increase slightly due to higher internal friction in the tire compound. The change is usually less than 20% over the normal speed range.

Why is my measured Crr higher than the typical value?

Possible reasons: you are measuring on a rough surface, tire pressure is low, the load is higher than rated, or bearing friction is included in the measurement. Also, a new tire has higher Crr than a broken-in one. Check your units and measurement method first.

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in f | Force (N) | N | 10 | 0
in w | Load (N) | N | 100 | 0
in r | Wheel radius (m) | m | 0.3 | 0
out crr | Rolling resistance coefficient | - | f / w | 3
out fr | Rolling resistance force (N) | N | f | 2