Rolling Resistance Calculator works out the force of rolling resistance from mass and a coefficient, or a coefficient from tire pressure. It also gives power and coasting distance.
Pick a tire and surface for the coefficient, or type your own value.
Slope, Wheels and Units
Step-by-Step Working
- Known values in SI units: mass = 1,500 kg, g = 9.81 m/s², slope = 0°, speed = 25 m/s
- Load on the ground: N = m × g × cos θ = 14,710 N
- Rolling resistance: F = Crr × N = 0.01 × 14,710 = 147.1 N
- Power at that speed: P = F × v = 147.1 × 25 = 3,677.5 W
- Result: 147.1 N (33.07 lbf), needing 3.68 kW to hold 90 km/h
Force on Other Surfaces
| Tire and Surface | Crr | Rolling Force |
|---|---|---|
| Steel wheel on rail | 0.0015 | 22.06 N |
| Bike tire on concrete | 0.002 | 29.42 N |
| Bike tire on asphalt | 0.004 | 58.84 N |
| Truck tire on asphalt | 0.008 | 117.68 N |
| New car tire, typical | 0.01 | 147.1 N |
| Car tire on concrete | 0.0125 | 183.87 N |
| Car tire on asphalt | 0.02 | 294.2 N |
| Car tire on worn cobbles | 0.03 | 441.3 N |
| Car tire on firm sand | 0.06 | 882.6 N |
| Car tire on loose sand | 0.3 | 4,413 N |
Power-Speed Graph
What the Rolling Resistance Calculator Finds
Rolling resistance is the force that opposes a wheel as it rolls. It comes mainly from the tire and the surface flexing where they touch, which turns some of the motion into heat. It is much smaller than sliding friction, but it acts the whole time a vehicle is moving.
The Rolling Resistance Calculator has four settings under Calculate. Force From a Coefficient is the usual one. Coefficient From a Force works back from a measured pull. Car Tire From Its Pressure estimates the coefficient from tire pressure and speed, and Wheel Radius Method suits hard wheels such as steel on rail.
It opens with a 1,500 kg car on typical new tires, at a coefficient of 0.01. The rolling resistance is 147.1 N, or 33.07 lbf. Holding 90 km/h against that force takes 3.68 kW and uses 40.86 Wh for every kilometer. With no brakes and no air drag, the car would coast 3.19 km before stopping.
Rolling Resistance Formula
To calculate rolling resistance, multiply the rolling resistance coefficient by the load pressing the wheels onto the ground. On a slope of angle θ the load is slightly less than the weight. The coefficient, written Crr, has no units.
$$F = C_{rr} \, m \, g \cos\theta$$
Turned around, the same line gives the coefficient from a measured force. A steady pull of 250 N on a 1,500 kg car means a coefficient of 0.017. This is the Coefficient From a Force setting of the Rolling Resistance Calculator.
$$C_{rr} = \frac{F}{m \, g \cos\theta}$$
The formula for rolling friction on hard wheels is often written with a length in place of the coefficient. The rolling friction length b is divided by the wheel radius r, as in the Engineering ToolBox reference. A steel wheel of 460 mm radius with b = 0.5 mm has a coefficient of 0.00109.
$$F = \frac{b \, m \, g}{r}$$
The power needed to overcome the force is the force times the speed. The force stays the same at any speed in the basic model, so the power rises in a straight line. Doubling the speed doubles the power lost to the tires.
$$P = F v$$
Rolling Resistance Coefficient Table
The table lists the presets in the Rolling Resistance Calculator beside the published range each one comes from. The last column is the force on a 1,500 kg load on level ground, which is what the surface table inside the tool shows for the opening example.
| Tire and surface | Published range | Preset | Force at 1,500 kg |
|---|---|---|---|
| Steel wheel on rail | 0.001 to 0.002 | 0.0015 | 22.06 N |
| Bike tire on concrete | 0.002 | 0.002 | 29.42 N |
| Bike tire on asphalt | 0.004 | 0.004 | 58.84 N |
| Truck tire on asphalt | 0.006 to 0.01 | 0.008 | 117.68 N |
| New car tire, typical | 0.007 to 0.014 | 0.01 | 147.1 N |
| Car tire on concrete or new asphalt | 0.01 to 0.015 | 0.0125 | 183.87 N |
| Car tire on tar or asphalt | 0.02 | 0.02 | 294.2 N |
| Car tire on worn cobbles | 0.03 | 0.03 | 441.3 N |
| Car tire on firm sand | 0.04 to 0.08 | 0.06 | 882.6 N |
| Car tire on loose sand | 0.2 to 0.4 | 0.3 | 4,413 N |
The surface matters as much as the tire. Loose sand has 15 times the drag of asphalt. The opening preset is for the tire itself. A Transportation Research Board report found that most new passenger tires measure between 0.007 and 0.014, with an average near 0.01. The 0.02 asphalt figure suits a rougher tar surface.
| Car tire coefficient | Rolling force | Power at 90 km/h | Energy per km |
|---|---|---|---|
| 0.007 | 102.97 N | 2.57 kW | 28.6 Wh |
| 0.01 | 147.1 N | 3.68 kW | 40.86 Wh |
| 0.014 | 205.94 N | 5.15 kW | 57.21 Wh |
| 0.02 | 294.2 N | 7.35 kW | 81.72 Wh |
Tire Pressure and Rolling Resistance
Higher tire pressure lowers rolling resistance, because a firmer tire flexes less. The third setting of the Rolling Resistance Calculator uses a published formula for air-filled car tires on a dry road. Pressure p is in bar and speed v is in km/h.
$$C_{rr} = 0.005 + \frac{0.01 + 0.0095 \left(\frac{v}{100}\right)^2}{p}$$
| Tire pressure | Coefficient at 90 km/h | Force at 1,500 kg |
|---|---|---|
| 1.5 bar (21.8 psi) | 0.0168 | 247.08 N |
| 2 bar (29 psi) | 0.01385 | 203.7 N |
| 2.5 bar (36.3 psi) | 0.01208 | 177.67 N |
| 3 bar (43.5 psi) | 0.0109 | 160.31 N |
| 3.5 bar (50.8 psi) | 0.01006 | 147.92 N |
A tire run at 1.5 bar has 39% more rolling resistance than the same tire at 2.5 bar. The formula also lets the coefficient rise with speed. At 2.5 bar it is 0.00934 at 30 km/h, 0.01208 at 90 km/h and 0.01755 at 150 km/h. Always keep to the pressure the vehicle maker lists.
Bike, Truck and Rail Examples
As a rolling resistance calculator for a bike, enter the rider and bike together. An 85 kg total on asphalt, at a coefficient of 0.004, meets 3.33 N. At 30 km/h that costs 27.8 W. Smooth concrete at 0.002 halves it to 13.9 W, and a rough road at 0.008 doubles it to 55.6 W.
Trucks have low coefficients but huge loads. A 36,000 kg truck at 0.008 has 2,824 N of rolling resistance and needs 70.6 kW at 90 km/h to overcome it. At 0.006 that falls to 53 kW. This is why tire makers such as Michelin publish comparison tools for their truck treads. Any coefficient from such a chart can be typed in here.
Steel on rail is the lowest of all. An 80 tonne rail car at 0.0015 has only 1,177 N of rolling resistance. That is eight times the force on the 1,500 kg car in the opening example, for 53 times the mass.
Grade, Total Resistance and Coasting
A rolling resistance coefficient reads directly as a slope. A coefficient of 0.01 feels the same as a steady 1% climb, and the car will roll on its own down anything steeper than 0.57°. The second card of the Rolling Resistance Calculator gives both.
The total resistance on a hill adds the pull of gravity along the slope. On a 5% climb the 1,500 kg car gains 734.58 N, for a total of 881.5 N, six times its drag on the level. Air drag comes on top of that and grows with the square of the speed, as the Free Fall with Air Resistance Calculator shows for a falling body. Forces on a slope alone are covered by the Inclined Plane Calculator.
| Coefficient | Coasting distance from 90 km/h | Time to stop |
|---|---|---|
| 0.0015 | 21.24 km | 28.33 min |
| 0.004 | 7.97 km | 10.62 min |
| 0.01 | 3.19 km | 4.25 min |
| 0.02 | 1.59 km | 2.12 min |
| 0.06 | 531 m | 0.71 min |
Coasting distance does not depend on the mass, only on the coefficient and the starting speed. The Rolling Resistance Calculator leaves out air drag in these figures, so a real vehicle stops sooner.
Lowering Rolling Resistance
How do you lower rolling resistance?
Keep the tires at the listed pressure, carry less weight, and choose tires with a lower coefficient. The road matters too, since smooth concrete beats rough asphalt. Rolling resistance cannot be eliminated. Even a steel wheel on a steel rail keeps a coefficient of 0.001 to 0.002.
Is lower rolling resistance better?
For fuel or battery range, yes. The Transportation Research Board report found that a 10% cut in rolling resistance improves the fuel economy of most passenger vehicles by about 1 to 2%. A low rolling resistance tire is simply one with a lower coefficient than usual for its type.
There is no way to identify one by looking at it. The coefficient the maker publishes, or an efficiency grade where tires carry one, is the only guide. Grip and wear are separate properties and need checking separately.
How is rolling resistance tested?
Tire makers measure it on a rotating drum under standard methods such as SAE J2452. A rough test at home is to measure the steady pull that keeps a vehicle rolling slowly on level ground. Enter that pull under Coefficient From a Force, and the Rolling Resistance Calculator names the closest listed surface.
What is the difference between rolling resistance and friction?
Sliding friction resists two surfaces rubbing past each other. Rolling resistance comes from deformation, with no sliding at the contact. For rubber on a dry road the sliding coefficient is many times the rolling one, which is why a skidding car stops in a far shorter distance than a coasting one. Sliding cases belong in the Friction Calculator.
Everyday examples of rolling friction include car and bike tires on a road, train wheels on rails, ball bearings in a hub, a suitcase on its wheels and a bowling ball on a lane. Each loses a little energy at the contact as it rolls.