Rolling Resistance Calculator
Enter your vehicle mass, surface type, speed, and road slope to instantly calculate rolling resistance force, the power consumed overcoming it, grade resistance on slopes, and the total tractive force required. Choose from 13 built-in tire-surface presets or enter a custom coefficient. Switch between metric and imperial units at any time.
What is rolling resistance?
Rolling resistance is the force that opposes the motion of a wheel, tire, or ball rolling over a surface. It arises primarily from the deformation of the tire (or wheel) and the surface as they make contact: energy is absorbed in compressing and reforming these materials with each rotation, and that energy is lost as heat rather than returned to forward motion. Unlike sliding (kinetic) friction, rolling resistance does not depend on surface roughness at the macro level; it depends instead on the elastic properties of the contact materials, tire inflation pressure, load, speed, and temperature. In vehicles, rolling resistance typically accounts for 15-30% of total energy consumption at highway speeds for cars, and an even higher fraction at lower speeds where aerodynamic drag is smaller.
The rolling resistance formula
The basic formula is Frr = Crr x N, where Frr is rolling resistance force in Newtons, Crr is the dimensionless coefficient of rolling resistance, and N is the normal force (the component of vehicle weight perpendicular to the road). On a flat road, N = m x g where m is mass in kilograms and g is gravitational acceleration (9.81 m/s2). On a slope of angle theta, the normal force becomes N = m x g x cos(theta), and an additional grade resistance force Fgrade = m x g x sin(theta) acts along the road. The power consumed by rolling resistance is P = Frr x v, where v is vehicle speed in metres per second. Doubling speed doubles rolling resistance power loss even though the force itself stays constant, because power is force times velocity.
What affects rolling resistance?
Tire inflation pressure is the single most controllable factor: an underinflated tire deforms more under load, increasing Crr and wasting energy. Load matters too: heavier vehicles produce higher normal forces and therefore higher rolling resistance forces, though Crr itself changes only slightly with load. Speed has a secondary effect at highway speeds via tire heating, but the basic model treats Crr as a constant. Tire construction is critical: a tire with stiffer, thinner sidewalls and a harder tread compound loses less energy per revolution (low-rolling-resistance tires). Surface hardness also plays a major role, which is why steel rail wheels on smooth steel rails achieve a Crr below 0.001 while car tires on loose sand can reach 0.15 or more. Temperature also affects rubber stiffness: Crr is typically higher when tires are cold.
Rolling resistance vs. aerodynamic drag
Rolling resistance force is essentially constant with speed (in the basic model), but aerodynamic drag force grows with the square of speed. At low speeds (city driving, below about 60 km/h) rolling resistance is the dominant drive-cycle loss for most vehicles. Above 80-100 km/h aerodynamic drag typically exceeds rolling resistance. For electric vehicles and cyclists, minimizing Crr delivers the biggest fuel (energy) savings in urban or stop-and-go conditions. On a grade, grade resistance can dwarf both: a 1500 kg car on a 5% incline generates about 736 N of grade resistance, compared to roughly 191 N of rolling resistance on asphalt, so the grade force is almost 4 times larger.
Typical rolling resistance coefficients (Crr)
| Surface / Tire type | Crr range | Typical Crr | Notes |
|---|---|---|---|
| Steel wheels on steel rails (clean) | 0.0001-0.0010 | 0.0005 | Lowest achievable Crr; railways |
| Steel wheels on steel rails (dirty) | 0.003-0.007 | 0.005 | Contaminated tram rails |
| Bicycle tire, wooden velodrome track | 0.001-0.002 | 0.001 | Racing conditions |
| Bicycle tire, concrete | 0.002-0.004 | 0.002 | Hard smooth surface |
| Bicycle tire, asphalt | 0.003-0.006 | 0.004 | Typical road riding |
| Bicycle tire, rough road | 0.006-0.012 | 0.008 | Unpaved or worn surface |
| Truck tires on asphalt | 0.004-0.010 | 0.006 | Heavy vehicle, hard surface |
| Car tires on concrete | 0.008-0.015 | 0.011 | Smooth concrete pavement |
| Car tires on asphalt | 0.010-0.016 | 0.013 | Most common passenger vehicle case |
| Car tires on gravel | 0.015-0.030 | 0.020 | Unpaved gravel road |
| Car tires on cobblestones | 0.020-0.040 | 0.030 | Old paving stones |
| Car tire on solid sand | 0.040-0.080 | 0.060 | Compacted sand surface |
| Car tire on loose sand | 0.100-0.200 | 0.150 | Beach or desert driving |
Representative values from engineering literature. Actual Crr varies with tire pressure, load, speed, and temperature.
Frequently asked questions
What is the coefficient of rolling resistance (Crr)?
Crr is a dimensionless number that represents the ratio of rolling resistance force to normal force. A lower Crr means less energy is lost per unit of load. Steel rail wheels achieve Crr values as low as 0.0001-0.001, while car tires on asphalt are typically 0.010-0.016. You can look up Crr for your tire-surface combination in the reference table above, or enter a custom value.
How does slope affect rolling resistance?
A slope changes the normal force (the component of weight perpendicular to the road surface). On a 5% grade (about 2.86 degrees), cos(2.86 deg) is approximately 0.9988, so the normal force and rolling resistance force are almost unchanged. However, the grade also adds a separate gravity component (grade resistance = m x g x sin(angle)) that can be much larger than the rolling resistance itself, which is why hills dramatically increase the total force the engine must provide.
How do I reduce rolling resistance?
Keep tires inflated to the manufacturer-recommended pressure (or slightly higher for long highway trips). Choose low-rolling-resistance (LRR) tires when replacing tires. On smooth, hard surfaces Crr is inherently lower than on gravel or sand. Avoid heavy loads when possible. At lower speeds, reducing rolling resistance has a bigger relative impact on efficiency than at highway speeds where aerodynamic drag dominates.
What is grade resistance and how is it different from rolling resistance?
Grade resistance is the component of gravity acting against forward motion along a slope: Fgrade = m x g x sin(theta). Rolling resistance is the energy-dissipation force from tire deformation: Frr = Crr x N. Both oppose forward motion uphill, but grade resistance disappears on a flat road and actually aids motion downhill. Rolling resistance always opposes motion regardless of slope direction.
Why does speed increase power loss but not rolling resistance force?
Power is force multiplied by velocity (P = F x v). Since rolling resistance force (Frr = Crr x m x g) does not depend on speed in the basic model, power loss scales linearly with speed. Driving twice as fast doubles the power wasted on rolling resistance, even though the force is the same. In contrast, aerodynamic drag force itself grows with the square of speed, so its power loss grows with the cube of speed.