How to use it
- Choose What to work out: a power for a speed, or a speed for a power.
- Type the Speed or the Rider power, the Gradient, and the Rider and bike mass.
- Type Rolling resistance (Crr), Drag area (CdA) and the Drivetrain.
- Read the answer, open Working for each part, and see Power and speed by gradient.
The physics model
The power at the pedals is the power at the wheel divided by the drivetrain efficiency. At the wheel, power goes into air drag, rolling resistance and climbing. The article writes the slope as rise over run, and gives an air density of 1.225 kg/m³ at sea level and 15 °C.
P = (PD + PR + PS) ÷ η
PD = ½ × 1.225 × CdA × v³
PR = v × m × 9.8 × Crr × cos(arctan s)
PS = v × m × 9.8 × sin(arctan s)The figures the source gives
- Air density 1.225 kg/m³ at sea level and 15 °C, and gravity 9.8 m/s².
- Crr from 0.003 to 0.006, measured on rollers at the maximum recommended tyre pressure. The article says it rises by about half at 10 m/s; the calculator keeps it constant.
- Drivetrain losses of 1–7 % for derailleurs, 4–12 % for a chain with a 3-speed hub and 10–20 % for a shaft drive with a 3-speed hub.
- No typical CdA for a rider's position. The article gives a drag coefficient of about 1 for an upright rider, but no frontal area, so the drag area is for you to type.
What the calculator does not cover
- Wind. Speeds are over the ground in still air.
- Acceleration. The speed is steady, so the model has no acceleration term.
- Altitude and temperature, which change the air density.
- A descent: on a downhill the climbing term is negative, and the model is not set up for it. The gradient starts at 0 %.
Worked example: 30 km/h up a 5 % climb
At 30 km/h (8.33 m/s) on 5 %, the air drag is 124 W, the rolling resistance 29 W and the climb 326 W. Together that is 479.7 W at the wheel. With the 4 % derailleur loss the rider needs 479.7 ÷ 0.96 = 500 W.
On the flat, the same speed needs 160 W.
| Gradient | Rider power at 30 km/h |
|---|---|
| 0 % | 160 W |
| 5 % | 500 W |
Frequently asked questions
Why is the drag area not given?
The article gives a drag coefficient of about 1 for an upright rider, but no frontal area and no typical drag area. Measure or estimate your own CdA. Drag grows with the cube of speed, so the drag area matters more the faster you ride.
Why is the power at the pedals more than the power at the wheel?
The drivetrain loses part of the power, so the rider produces more than reaches the wheel. The calculator divides the wheel power by the efficiency, as the article's equation does.
What does the gradient mean in the formula?
The slope is rise over run, so 5 % means a rise of 5 m for every 100 m along the road. The formula uses the angle whose tangent is that slope.
How does the calculator find the speed for a power?
Drag grows with the cube of speed, so the power cannot be turned into a speed by a simple division. The calculator halves a range of speeds until it finds the one that gives the power you typed.
Is this the same as a power meter reading?
No. A power meter measures what the rider puts out. This calculator works out the power that a model of the road and the bike needs, and the model leaves out wind, acceleration and altitude.
Sources
Figures and text last checked on Tuesday, November 10, 2026.