The rolling resistance calculator above computes the force that resists a wheel rolling freely along a surface, the power a vehicle must produce continuously to keep that wheel turning, and the energy the loss consumes over a fixed distance. Rolling resistance is not friction in the schoolbook sense. Nothing is sliding. The force exists because the tyre and the road deform as the contact patch moves through the rubber, and the material does not give back all the energy it stored during that deformation. That lost fraction, called hysteresis, is where almost all of the loss comes from.
Arb Digital publishes free engineering calculators that keep separate mechanisms visibly separate. This page reports the gradient force alongside the rolling term rather than folding them together, because on any slope worth mentioning the gravity component is many times larger than the rolling one and people who add them into a single number lose the ability to see which lever actually matters.
What This Rolling Resistance Calculator Does
The hero figure is the rolling resistance force in newtons: the steady backwards push a freely rolling vehicle feels from the road. Everything else follows from it. The power figure multiplies that force by road speed, giving the watts the drivetrain must deliver purely to cancel the rolling loss, before aerodynamics, before transmission losses, before anything else.
The energy figure converts the same force into the work needed to travel a hundred kilometres, which is the number that actually shows up in fuel and battery consumption. Because force multiplied by distance is work, and because rolling resistance barely changes with speed, this figure is almost independent of how fast you drive. The axle torque figure converts the force into the twisting moment the driven wheels must supply against it, using the loaded rolling radius you enter. And the gradient figure reports the separate gravity term, so the slope contribution is never quietly hidden inside the rolling number.
How to Use It
- Enter the mass that is actually on the tyres. Kerb weight is the wrong figure for a loaded vehicle. Add the payload, the passengers and the fuel, because rolling resistance is proportional to the load pressing down.
- Get a coefficient you can defend. Use the tyre maker's measured value, a regulated label figure, or your own coast-down test. A guessed coefficient makes every downstream number a guess too.
- Set the speed in whatever unit you have. The force does not change much with speed, but the power does, in direct proportion.
- Add the gradient if you are on a slope. Enter it as a percentage. The tool tilts the normal force correctly and reports the gravity term on its own.
- Measure the loaded wheel radius for the torque figure. Take it from hub centre to ground with the vehicle at working weight, not from the nominal tyre diameter, which is always larger than the loaded radius.
The Formula: How Rolling Resistance Is Calculated
The working relation is Frr = Crr × N, where N is the normal force between tyre and road. On level ground N = mg. On a slope of angle θ the normal force becomes mg cos θ, and a separate gravity force mg sin θ acts along the road surface. A gradient given as a percentage p converts to an angle with θ = arctan(p ÷ 100).
Power follows from P = Frr × v with speed in metres per second. Energy over a distance d is simply E = Frr × d, since the force is constant. Axle torque is T = Frr × r for a loaded rolling radius r. The equivalent deceleration a coasting vehicle feels is a = Frr ÷ m, which on the flat reduces to Crr × g and is therefore independent of mass entirely.
The coefficient itself is defined as rolling resistance divided by wheel load, and the National Academies' review of rolling resistance, traction and wear performance of passenger tires sets out both the definition and the measured spread across the market. Because the relationship with load is close to linear, treating the coefficient as a constant is a good approximation across the normal working range of a tyre.
Work the defaults through by hand. A mass of 1,500 kg on level ground gives a normal force of 1,500 × 9.80665 = 14,709.98 N. With a coefficient of 0.010 the rolling resistance is 147.10 N. At 100 km/h, which is 27.778 m/s, the power is 147.10 × 27.778 = 4,086 W, a little over four kilowatts. Over 100 km the work done is 147.10 × 100,000 = 14.71 MJ, which is 4.086 kWh — and, as expected, exactly the four-kilowatt figure sustained for the one hour that journey takes. Against a loaded radius of 0.32 m the axle must supply 147.10 × 0.32 = 47.07 N·m. The equivalent coasting deceleration is 0.0981 m/s².
Why This Is Not the Same Thing as Friction
The arithmetic looks identical to sliding friction — a dimensionless coefficient multiplied by a normal force — and that resemblance causes real confusion. The physics is different. Sliding friction arises from surfaces moving across one another and dissipating energy at the interface. Rolling resistance arises from a body being repeatedly squashed and released, and losing a fraction of the stored elastic energy each cycle because the material is not perfectly elastic.
The practical consequences diverge sharply. Sliding friction coefficients for rubber on road sit around 0.7 to 1.0. Rolling resistance coefficients for the same tyre on the same road are two orders of magnitude smaller. If you are analysing a wheel that is skidding, locked, or being braked hard, the friction force calculator is the right page and this one is not, because the moment a tyre slides the loss mechanism changes completely — and OpenStax's treatment of static and kinetic friction in University Physics deliberately covers only that sliding case.
There is a second consequence that surprises people. Because the rolling loss is a bulk material property, it responds to things a surface-friction model has no vocabulary for: inflation pressure, tyre temperature, sidewall construction, tread depth and rubber compound. Nothing about the road surface texture changes those. This is why underinflation increases rolling resistance so much, and why a tyre measured cold gives a pessimistic answer compared with the same tyre after twenty minutes of running.
Where Rolling Resistance Stops Dominating
Rolling resistance is essentially flat with speed while aerodynamic drag rises with the square of speed. That single fact organises the whole subject. At walking and town speeds the rolling term is the larger of the two by a wide margin. Somewhere in the middle of the normal road-speed range the two curves cross, and above that point every additional unit of speed costs disproportionately more in drag.
The practical reading is about where to spend effort. On a delivery van doing short urban runs with constant stops, tyre choice and inflation pressure are worth more than bodywork. On a vehicle that spends its life at motorway speed, the same tyre improvement is diluted by a drag term that has grown far larger. Running the same speeds through the drag force calculator alongside this page shows the crossover for your own frontal area and drag coefficient rather than a remembered rule of thumb.
There is also a stop-start effect that neither term captures. In heavy traffic a large share of the energy goes into repeatedly accelerating the mass and then throwing that kinetic energy away as brake heat. The kinetic energy calculator quantifies how much is at stake in a single stop, and it is often larger than several kilometres of rolling loss.
Measuring Your Own Coefficient by Coast-Down
Published coefficients are averages from standardised drum tests. Your vehicle on your surface is a different measurement, and a coast-down test on a level road is the accessible way to get it. Bring the vehicle to a steady speed, select neutral, and record the speed against time as it slows.
The subtlety is that the deceleration you measure contains both rolling and aerodynamic terms, and separating them takes more than one run. At low speed, where drag is small, the deceleration approaches Crr × g and the coefficient falls out directly. Fitting the whole curve, with a constant term and a term proportional to speed squared, recovers both. Drivetrain drag in neutral, wheel bearing losses and any residual brake contact are all lumped into whatever the fit calls rolling resistance, so the number is honest about the vehicle rather than about the tyre alone.
Two practical warnings. A road that looks flat rarely is, and a gradient of even a few tenths of a percent contributes a force comparable to the entire rolling term — run the test in both directions and average. And wind matters enormously, because a light headwind changes the drag term without changing the rolling term, which corrupts exactly the separation you are trying to make.
What Moves the Coefficient in Practice
Inflation pressure is the largest lever a driver controls. A softer tyre deforms more through each rotation, so more rubber is worked and more energy is lost to hysteresis. This is also why an underinflated tyre runs hot: the missing energy has to go somewhere, and it goes into the carcass.
Temperature moves the number in the opposite direction. Rubber becomes less lossy as it warms, so a tyre measured in the first minutes of a journey shows a noticeably higher coefficient than the same tyre at steady operating temperature. Standardised tests specify a warm-up period precisely so that this effect does not contaminate comparisons.
Surface matters more than tyre construction on anything unpaved. On smooth asphalt the tyre does nearly all the deforming. On gravel, sand or soft ground the surface deforms too, the wheel is effectively climbing continuously out of the depression it makes, and the effective coefficient can rise by a factor of ten or more. That regime is not well described by a single constant and the numbers on this page should be treated as a rough lower bound there.
Load has a mild secondary effect on top of the proportional one. Doubling the load slightly more than doubles the resistance in most tyres, because the carcass is worked harder per unit of load. For engineering estimates the linear model is normally close enough, and the normal force calculator handles the load side when the geometry is not simply flat ground.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using a sliding friction coefficient — a value near 0.8 belongs to a skidding tyre, not a rolling one, and produces a rolling resistance figure roughly eighty times too large.
- Entering kerb weight for a loaded vehicle — the force is proportional to what is actually pressing on the tyres, so a forgotten tonne of payload is a forgotten tonne of resistance.
- Adding the gradient force into the rolling number — on any real slope gravity dominates, and merging the two hides the fact that better tyres cannot help you climb a hill.
- Assuming the coefficient is a property of the road — it is mostly a property of the tyre, its pressure and its temperature, which is why the same road gives very different answers to different vehicles.
- Using nominal tyre radius for torque — a loaded tyre sits measurably lower than its unloaded radius, and the difference propagates straight into the axle torque figure.
Related Free Tools From Arb Digital
The inclined plane calculator works the full force balance on a slope and the horsepower calculator converts the power figure into the units engine data is usually quoted in. For the drivetrain side, the gear ratio calculator takes axle torque back to the engine, and the fuel cost calculator puts a price on the energy. Everything Arb Digital publishes sits on the free online tools hub.
Frequently Asked Questions
It is the force that opposes a wheel rolling freely over a surface. It comes almost entirely from hysteresis: the tyre and, on soft ground, the surface deform as the contact patch passes through them, and the material does not return all the energy it absorbed. That lost fraction appears as a steady retarding force and as heat in the tyre carcass.
No, although the arithmetic looks identical. Sliding friction dissipates energy at an interface where two surfaces move across each other. Rolling resistance dissipates it inside the bulk of a deforming material with no sliding at all. The coefficients differ by roughly two orders of magnitude, so using one in place of the other gives an answer that is wrong by a very large factor.
Only weakly across normal road speeds, which is why treating the coefficient as constant is a reasonable working model. There is a mild rise at high speed as the carcass is flexed more often per second, and a sharp rise near the tyre's speed limit as standing waves form in the sidewall. Aerodynamic drag, by contrast, rises with the square of speed, so drag overtakes rolling resistance as speed increases.
A softer tyre deforms more through every rotation, so more rubber is worked and more energy is lost to hysteresis. That raises the rolling resistance coefficient and therefore the force, the power and the energy per kilometre. The same lost energy also heats the carcass, which is why underinflated tyres run hot and wear their shoulders.
Either take the manufacturer's measured value for the fitted tyre, or run a coast-down test. Bring the vehicle to speed on a level road, select neutral, and record speed against time. At low speed the deceleration approaches the coefficient multiplied by gravity. Run the test in both directions and average, because a gradient of a fraction of a percent is enough to corrupt the result.
Not from rolling resistance alone. The retarding force grows in proportion to mass, but so does the inertia resisting the change in speed, so the deceleration works out as the coefficient multiplied by gravity regardless of mass. Aerodynamic drag does not scale with mass, though, so in practice a heavier vehicle coasts further because the drag term is diluted.
Because on a slope it dominates. The gravity component along the road is the mass multiplied by gravity multiplied by the sine of the slope angle, and even a modest gradient makes it several times the rolling term. Merging them into one number hides which one you can actually do something about: tyre choice moves the rolling term and cannot touch the gravity term at all.
This tool is provided for educational and preliminary engineering use. It models rolling resistance with a constant coefficient, which is an approximation that degrades on soft or unpaved surfaces and near a tyre's speed rating. Use the tyre manufacturer's measured data or your own instrumented test for design work.
