Compute the force of rolling resistance (F = Crr × m × g), the power it eats at speed, the extra force on a hill, and how far you coast from speed — with honest, sourced Crr presets from rail (0.0015) to loose sand (0.30).
F = Crr × m × g on flat ground.
Empirical car-tire model (EngineeringToolBox): c = 0.005 + (1/p) × (0.01 + 0.0095 × (v/100)²), p in bar, v in km/h.
P = F × v. Force is speed-independent; power grows linearly with speed.
Uphill: F = Crr·m·g·cosθ + m·g·sinθ. Downhill (moving down): rolling resists while gravity assists.
Same vehicle, same speed — every Crr preset side by side.
| Surface / tire | Crr | Force (N) | Power (W) | Energy / 100 km (MJ) |
|---|
Crr values are representative midpoints; published ranges are noted in the FAQ. Sources: EngineeringToolBox rolling-friction table, Wikipedia rolling-resistance table, EU passenger-car tyre label (class A).
How far you roll from speed v₀ to a full stop if only rolling resistance slows you: s = v₀² / (2 × Crr × g).
The rolling resistance force is F = Crr × N, where Crr is the dimensionless coefficient of rolling resistance and N is the normal force (m × g on flat ground). Power is P = F × v. On a slope of angle θ: F = Crr·m·g·cosθ ± m·g·sinθ (+ uphill, − downhill). Coast-down assumes constant deceleration a = Crr·g, giving s = v₀²/(2a) and t = v₀/a.
Crr is not a universal constant: it depends on tire construction, inflation pressure, speed, temperature, load, and the surface. The presets are representative values from published tables (see FAQ); for design work, measure or look up your specific tire.
Rolling resistance is the force that resists the motion of a body rolling on a surface. On flat ground it is F = Crr x m x g, where Crr is the dimensionless coefficient of rolling resistance, m is mass, and g = 9.80665 m/s2. Example: a 1000 kg car on asphalt with Crr = 0.01 needs F = 0.01 x 1000 x 9.80665 = 98.07 N (about 22.05 lbf) of force just to keep rolling steadily.
Crr is a dimensionless number rating a tire-surface pair. Typical published values: steel rail wheel on steel rail 0.001-0.002; bicycle tire on smooth asphalt 0.004; low-resistance tubeless tires 0.002-0.005; truck tire on asphalt 0.006-0.01; ordinary car tire on concrete or new asphalt 0.01-0.015; car tire on worn asphalt or tar 0.02; car tire on rolled gravel 0.02; car tire on loose sand 0.2-0.4. The EU passenger-car tyre label puts its most efficient class A at Crr of 0.0065 or below. Sources: EngineeringToolBox rolling-friction table and the Wikipedia rolling-resistance table. These are representative ranges, not constants - real tires vary with construction, load, pressure, and temperature.
Take a 1500 kg car on new asphalt (Crr = 0.012). Step 1: weight N = m x g = 1500 x 9.80665 = 14709.98 N. Step 2: F = Crr x N = 0.012 x 14709.98 = 176.52 N. Step 3 (optional): energy per 100 km = F x distance = 176.52 N x 100000 m = 17651970 J = 17.65 MJ, which is 17.65 / 3.6 = 4.90 kWh per 100 km. The Force tab above does this automatically, including imperial units.
No - the force itself is essentially independent of speed; what changes is the power. Power is P = F x v, so it grows linearly with speed. Example: the 98.07 N force above at 25 m/s (90 km/h) needs P = 98.07 x 25 = 2451.66 W, about 2.45 kW or 3.29 hp. Honest nuance: Crr itself creeps up slightly at high speed, which is why the tire-pressure model on this page takes speed as an input.
On a slope of angle theta, the normal force drops to m x g x cos(theta) and gravity adds a component along the slope: uphill F = Crr x m x g x cos(theta) + m x g x sin(theta). Example: 1500 kg car, Crr 0.012, 6% grade (theta = 3.43 degrees). Rolling component: 176.20 N. Grade component: 881.01 N. Total uphill force: 1057.22 N - the hill term is about 5 times the rolling term. Downhill is the reverse: at 3% grade moving down, the net force is -264.66 N, meaning gravity wins and the vehicle would accelerate unless braked.
With only rolling resistance slowing you, deceleration is constant at a = Crr x g, so distance s = v0^2 / (2 x Crr x g) and time t = v0 / (Crr x g). Example: coasting from 100 km/h (27.78 m/s) with Crr = 0.012 gives a = 0.11768 m/s2, s = 3278.4 m (about 3.28 km), and t = 236.0 s (about 3.9 minutes). This is idealized: real coast-downs are shorter because aerodynamic drag and any uphill slope also slow you down.
A steel wheel on a steel rail deforms almost nothing, so little energy is lost as heat: Crr is only 0.001-0.002. A rubber tire constantly squashes and un-squashes (hysteresis), throwing energy away as heat, giving Crr of 0.01-0.015 - roughly 8 times worse. Numbers for a 1500 kg vehicle at 90 km/h: rail gives 22.06 N and 551.6 W of rolling loss, while a car tire on concrete gives 176.52 N and 4413 W.
Higher pressure means less tire deformation and less hysteresis loss. An empirical estimate for air-filled car tires on dry roads (EngineeringToolBox) is c = 0.005 + (1/p) x (0.01 + 0.0095 x (v/100)^2), with p in bar and v in km/h. At 2.9 bar (42 psi) and 90 km/h this gives Crr = 0.0111; raising pressure to 3.5 bar drops it to 0.0101 (about 9% less); an under-inflated 1.5 bar tire at 60 km/h gives 0.0139. Real tires also depend on construction, tread, load, and temperature, so treat this as a starting point. See also the Tire Pressure Calculator linked below.
Rolling resistance force is roughly constant with speed, while aerodynamic drag grows with the square of speed (F_drag = 0.5 x rho x v^2 x Cd x A). The full steady-state road load is F = 0.5 x rho x v^2 x Cd x A + Crr x m x g. At low speed rolling resistance dominates; at highway speed drag usually dominates. The Power tab here covers the rolling term; the Drag Equation Calculator linked below covers the aerodynamic term.
Energy is force times distance: the 98.07 N example means 98.07 kJ per km, or 9.81 MJ per 100 km, which equals 2.72 kWh per 100 km. The 1500 kg car example wastes 17.65 MJ (4.90 kWh) per 100 km to rolling resistance alone - before aerodynamic drag, hills, and drivetrain losses are counted.
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