Rolling Resistance Calculator

Related Calculators

Rolling resistance coefficient, Crr (unitless): A small number that describes how much the tires resist rolling on a surface. In this calculator it is treated as constant for the chosen conditions [1].

Road grade (percent): Slope written as (rise/run) x 100. Example: 10% means 10 feet up for every 100 feet forward.

Road angle (degrees): The same slope written as an angle. The calculator converts between percent and degrees internally.

Normal force on the ground (N): The force pushing straight into the ground. On a slope it is m times g times cos(angle), so it is slightly smaller than m times g.

Rolling resistance force (N): The resisting force from rolling, modeled as Frr = Crr x (normal force) [1].

Power lost to rolling resistance (W): How fast energy is being used to overcome rolling resistance at your speed (power = force x speed).

Energy lost over distance (Wh): Total work done against rolling resistance over a trip length (energy = force x distance), shown in Watt-hours for easier battery comparisons.

Compare mode deltas (B minus A): Signed differences between setup B and setup A. Negative means setup B has lower rolling losses than setup A.

Mistake: Typing pounds (lb) into Total mass (kg) .
Fix: Either convert lb to kg first, or switch Mass/weight input type to weight-force and enter Total weight-force (lbf) .

Mistake: Leaving Rolling resistance coefficient, Crr (unitless) blank, or entering 0 or a negative value.
Fix: Enter a positive Crr (example: 0.005). The model needs Crr > 0 to represent a resisting force.

Mistake: Entering 5 into Road grade (percent) when you meant 5 degrees (or the other way around).
Fix: If you have degrees, set Grade input type to degrees and use Road angle (degrees) . If you have percent, keep percent.

Mistake: Using Compare mode but not entering Setup B: Crr (unitless) (or entering the same value as setup A by accident).
Fix: Enter a real setup B Crr, then read deltas as B minus A: a negative Power difference means setup B saves watts at the same speed.

Mistake: Seeing 0 W for Power lost to rolling resistance and thinking the calculator failed.
Fix: Check speed. A stationary setup has zero power loss. For a negative signed speed, the calculator uses its magnitude to represent reverse travel.

Mistake: Entering 0 for Distance for energy (miles) and expecting a meaningful energy number.
Fix: Leave distance blank to skip energy outputs (N/A), or enter a positive trip distance to get energy in J and Wh.

Steady-speed model: The calculator is a snapshot at one steady speed. It does not model extra losses during starts, stops, or changes in speed.

Crr is treated as constant: Real rolling resistance can change with tire pressure, temperature, tire construction, load, and road roughness, so real-world results can differ even if your Crr estimate is close [2][3].

Grade handling is only a normal-force correction: Grade changes rolling resistance here only through the cos(angle) factor in the normal force. This tool does not add climbing power (the separate uphill gravity term) and does not subtract it downhill.

Energy over distance is force times distance: The energy outputs assume the rolling resistance force stays constant over the whole distance. If conditions change during the trip (surface, pressure, load), real energy loss can change too.

Distance input unit is miles: By design, Distance for energy (miles) is interpreted as miles. Convert before entering if you have kilometers or meters.

Extreme slopes and unusual conditions: Road angles must lie strictly between -90 and 90 degrees. Very steep valid slopes still may not match reality well because tire slip and changing contact can dominate.

This calculator models rolling resistance as a force equal to Crr times the normal force, then converts that force into power at your speed and (optionally) energy over a distance [1].

1) Convert grade to a road angle

If you enter percent grade, it is converted to an angle using arctan(grade/100). If you enter degrees, it is converted to radians.

θ (road angle in radians) = arctan(grade_pct/100) [4]

θ (road angle in radians) = grade_deg * (π/180)

2) Compute normal force

Normal force is the part of weight that pushes straight into the ground. On a slope, only the perpendicular part counts.

N (normal force in N) = m (mass in kg) * g (m/s^2) * cos(θ)

If you choose weight-force input (lbf), the calculator converts lbf to Newtons first, then uses mass = weight_force_N / g so units stay consistent.

3) Compute rolling resistance force

Rolling resistance force is modeled with a constant coefficient [1].

Frr (rolling resistance force in N) = Crr * N

4) Convert speed to m/s and compute power

Power is force times speed. Speed is converted to meters per second and its magnitude is used, so rolling power loss stays nonnegative when a signed speed denotes reverse travel.

v (m/s) = speed_mph * 0.44704, or speed_kph / 3.6, or speed_mps

Prr (W) = Frr (N) * abs(v in m/s)

5) Energy over a distance (optional)

Work against a constant opposing force is force times distance, then Joules can be converted to Watt-hours.

d (m) = distance_mi * 1609.344

E (J) = Frr (N) * d (m)

E (Wh) = E (J) / 3600

Compare mode (A vs B)

Setup A uses your main Crr input. Setup B uses the setup B Crr. Deltas are computed as B minus A, so negative means B is lower.

ΔF (N) = Frr_B - Frr_A

ΔP (W) = Prr_B - Prr_A

ΔE (Wh) = EWh_B - EWh_A

Mini-example

Example (flat): mass = 85 kg, g = 9.80665 m/s^2, Crr = 0.005, speed = 20 mph. Then normal force N is about 85 x 9.80665 = 833.6 N, rolling resistance force Frr is about 0.005 x 833.6 = 4.17 N, speed is about 8.94 m/s, and rolling resistance power Prr is about 4.17 x 8.94 = 37.3 W. Over 10 miles, energy is about (4.17 N x 10 x 1609.344 m) / 3600 = 18.6 Wh.