Rolling Resistance Calculator - Crr, Force, and Presets

A rolling resistance calculator estimates the force a rolling object needs to overcome to keep moving on a surface. It takes a wheel/surface coefficient, the total mass, and the local gravity, and returns the rolling resistance force in newtons along with the normal force, the per-wheel force, and the power lost at the chosen cruising speed. Use it for physics homework, cycle-computer estimates, automotive fuel-economy checks, or rover studies.

• • Cycle and e-bike watts budgeting: Estimate how many watts a cyclist must spend to overcome rolling resistance at a given speed.
• • Automotive fuel-economy checks: Compare two tire presets to see whether low-rolling-resistance tires are worth the cost.
• • Train and rail freight studies: Compute the rolling resistance share of a train's tractive effort for locomotive sizing.
• • Off-planet rover and trailer loads: Reuse the same formula with lunar or Martian gravity to size rover wheels and motors.

Rolling resistance is one of three big losses a road vehicle fights, alongside aerodynamic drag and drivetrain friction. It scales with the weight on the wheels and the wheel/surface coefficient.

The formula is linear in mass and gravity, so the same calculator handles a 75 kg cyclist, a 1500 kg car, a 20000 kg train, and a 210 kg lunar rover with only the coefficient table and g changing.

Pair this rolling resistance calculator with the Friction Factor Calculator when a Darcy friction factor is needed for a related fluid-flow problem.

The calculator reads the wheel/surface preset, applies the matching coefficient, and multiplies by the normal force on the wheels. The result rows update instantly when the preset or gravity changes.

• Crr: Dimensionless coefficient of rolling friction for the chosen wheel/surface pair. The preset loads this; type a custom value when needed.
• m: Total mass of the rolling object in kilograms. For a bicycle it is rider plus bike; for a car it is curb weight plus payload.
• g: Local gravity in m/s^2. Earth sea level is 9.80665, the Moon about 1.62, Mars about 3.71.
• N: Normal force pressing the wheels into the surface, equal to m times g.
• F_RR: Rolling resistance force in newtons, equal to Crr times N.
• v: Cruising speed in m/s, multiplied by F_RR to give the power loss in watts.

The calculation runs every time an input changes, so the four result rows stay in sync with the form. The power loss row multiplies F_RR by speed, converting the force into watts.

For Moon or Mars rovers, change the gravity field. The preset still loads the same coefficient, but the force drops by the same factor that local gravity drops by.

According to Hyperphysics, the rolling resistance force equals the coefficient of rolling friction times the normal force, with a typical car tire on asphalt showing about 0.015

Above about 15 m/s the rolling resistance share drops and the Drag Equation Calculator takes over, so run both side by side for a complete resistance breakdown.

Rolling resistance looks like one number, but it sits on four ideas that show up in every physics treatment of the topic.

These four ideas explain why the formula is so simple. The coefficient absorbs what is special about the wheel/surface pair, the normal force captures the load, and the speed turns the force into a power loss.

Once a student can switch between newtons and watts, the same calculator doubles as a cycle-computer and a vehicle-energy study tool.

Reviewing the normal force in newtons alongside the Forces Newtons Laws Calculator helps connect the rolling resistance result to the broader Newton second law picture.

Pick a preset first, then enter mass, wheel count, and local gravity. The cruising speed field powers the watts row.

1. 1 Pick the wheel/surface preset: Start with the closest preset. The matching coefficient loads below. Car tire on asphalt is the default.
2. 2 Enter the total mass: Type the mass of the vehicle plus payload in kilograms. A road car is about 1500 kg, a cargo bike about 120 kg, a city bus about 12000 kg.
3. 3 Enter the number of wheels: Set the wheel count sharing the load. Most cars use 4. Trains count powered axles rather than individual wheels.
4. 4 Enter the local gravity: Use 9.80665 m/s^2 for Earth. Drop to 1.62 for the Moon, 3.71 for Mars, or 24.79 for Jupiter when sizing a rover.
5. 5 Enter the cruising speed: Type the constant cruising speed in m/s. 27 m/s is about 97 km/h, 8.3 m/s about 30 km/h.
6. 6 Read the rolling resistance force and per-wheel value: The primary card shows F_RR in newtons. The secondary rows show the normal force, per-wheel force, and power loss at the chosen speed.

A 75 kg cyclist plus a 10 kg bike rides a 28 mm tire on smooth asphalt at 8.3 m/s. Choosing Bicycle tire on asphalt sets Crr to 0.004; mass 85 kg, gravity 9.80665; the calculator returns F_RR = 3.33 N, per-wheel 1.67 N, and power loss of 27.7 W. That is a reasonable share of the cyclist's 200 to 250 W output.

Once the rolling resistance force and speed are known, the Work Energy Power Calculator converts the watts row into a per-kilometer energy budget for the same vehicle.

The rolling resistance force is small for a single wheel but adds up across a fleet. These benefits explain why a quick numerical estimate beats a guess.

• • Preset wheel/surface combinations: Load a published coefficient for bicycle, car, train, or off-road presets and switch between them to compare forces.
• • Mass, gravity, and wheel count inputs: Handle a 5 kg trailer wheel to a 12000 kg city bus from the same form, with per-wheel forces computed automatically.
• • Rolling resistance force in newtons: Read the answer in SI units, ready for a tractive-effort spreadsheet or to compare against aerodynamic drag.
• • Power loss at cruising speed: Convert the force into a watts budget at the chosen speed, the format cycle computers already use.
• • Custom coefficient mode: Switch to Custom and enter your own coefficient when working from a data sheet or measured drag run.
• • Earth, Moon, Mars, and custom gravity: Use the same calculator on other bodies by changing the gravity field, isolating gravitational scaling from wheel physics.

The combination of presets and a custom coefficient means the calculator serves physics students and practicing engineers.

Pair the rolling resistance output with a power or drag calculator when the rolling resistance share needs to be compared to the rest of the drivetrain.

When the rolling resistance force needs to be combined with a slope angle to find a net acceleration, the Kinematics Motion Calculator is the natural companion.

Rolling resistance looks like a single number, but it depends on the wheel/surface pair, load, inflation, temperature, and gravity. Two nominally identical vehicles can roll with different resistance.

• • The linear model F_RR = Crr * N treats the coefficient as constant. In reality Crr drifts with inflation, temperature, and speed, so treat the result as a first-order estimate.
• • For soft soil or sand the rolling resistance force can depend on how deep the wheel sinks, which the linear model does not capture. Use a terramechanics model when wheel sinkage is large.

These factors are not all equal. For a typical car tire on asphalt the material pair dominates the coefficient, the load decides the normal force, and gravity is essentially constant. For off-planet work, the load and gravity fields matter much more.

When a measured force disagrees with the calculator, check the assumed coefficient. Published values assume proper inflation, clean surfaces, and moderate speeds.

According to Wikipedia - Rolling resistance, rolling resistance is proportional to the normal force and independent of tire size for typical pneumatic tires

For climbs or banked surfaces the Resultant Force Calculator combines rolling resistance with the gravity component along the slope to give the net force on the vehicle.