Cycling Power Calculator
Estimate the power needed to ride at a steady speed from air drag, rolling resistance, bearing friction and gradient, using the Martin et al. road cycling model.
Result
Enter rider and bike mass, drag area cda, in m², rolling resistance coefficient crr, air density and drivetrain efficiency to see the result.
https://calcgallery.com/fitness-training/cycling-power-calculator/
How to use the Cycling Power Calculator
- Enter the speed you want to hold, the combined mass of rider and bike, and the road gradient.
- Enter your drag area (CdA), rolling resistance coefficient (Crr), the air density and your drivetrain efficiency. None is filled in, because each depends on you, your bike and the day.
- Optionally add a headwind, or a tailwind as a negative number, under more options.
- Read the power at the pedals and how it splits between air, rolling, bearings, climbing and the drivetrain.
The Martin model
In 1998 James Martin and colleagues published a model of the power needed to ride a road bike and checked it against power measured on the road. At a steady speed, with no acceleration, it adds four terms and divides by the drivetrain efficiency:
air = ½ × ρ × CdA × Va × |Va| × V, where Va = V + headwindrolling = Crr × m × g × cos(atan G) × Vbearings = V × (91 + 8.7 × V) ÷ 1000climbing = m × g × sin(atan G) × Vpedals = (air + rolling + bearings + climbing) ÷ efficiencyV is ground speed in metres per second, Va the speed of the air past the rider, m the mass of rider and bike, g standard gravity, 9.80665 m/s², and G the gradient as rise over run. The paper squares Va; the page keeps its sign, which gives the same answer whenever the air comes at you. In a tailwind faster than you ride, the air pushes you along, so the air term turns negative instead of adding power. The bearing term is the one piece with fixed coefficients: Martin and colleagues derived it from published measurements of bicycle wheel-bearing friction.
What the page leaves out
- Acceleration. The paper includes a kinetic energy term for speeding up and slowing down. At a steady speed it is zero, so the page leaves it out.
- Spoke drag. The paper adds a small aerodynamic term for spinning wheels, measured for its own wheels. It varies with the wheel, so the page leaves it to your CdA.
- Crosswinds. The paper adjusts drag area for the angle of the wind. The page takes only the head or tail component you enter.
- Drafting, gusts and cornering. None is modelled.
Reading the result
The breakdown matters as much as the total. On flat ground at racing speeds, air resistance is most of the power, so position and clothing change the answer more than anything else. On a climb the balance flips: the climbing term depends on total mass and gradient, and aerodynamics fades into the background. The drivetrain line shows the share lost between the pedals and the rear wheel at the efficiency you entered.
With your numbers
- At the wheel: air 192 W + rolling 31.4 W + bearings 1.8 W + climbing 0 W = 225.2 W
- Divided by 97% drivetrain efficiency: 232 W at the pedals
Quick reference
A model: it is only as good as the drag area, rolling resistance and air density entered. Gusts, drafting and acceleration are not included.
| Example | Power at the pedals |
|---|---|
| 30 km/h flat, CdA 0.32, Crr 0.004 | 143 W |
| 36 km/h flat, CdA 0.32, Crr 0.004 | 232 W |
| 40 km/h flat, CdA 0.25, Crr 0.004 | 250 W |
| 20 km/h up a 6% climb | 353 W |
| 12 km/h up a 10% climb | 291 W |
| 20 mph flat, CdA 0.3, Crr 0.004 | 164 W |
Common questions about the Cycling Power Calculator
- Where do I get CdA and Crr?
- Measured values are the most reliable. Martin and colleagues measured each rider's drag area in a wind tunnel and took Crr as the average of a published test of ten road tyres. Published figures for positions and tyres exist, but they vary so much with body size, clothing, tyre construction, pressure and road surface that the page does not choose one for you.
- Why does the power climb so fast with speed?
- Because air resistance power grows with the cube of speed. Going from 30 to 36 km/h is 20 percent faster but needs about 73 percent more power to push the air aside, on top of the smaller rolling and bearing terms that grow only in step with speed.
- What air density should I use?
- Air is less dense at altitude and on hot days, and denser in cold air near sea level. It can be worked out from the temperature, air pressure and humidity for your ride. Using a figure that is off by 5 percent changes the air term by 5 percent.
- Why is the answer zero on a steep descent?
- Going downhill, gravity pushes you along. When that push is larger than air drag, rolling resistance and bearing friction together, you would speed up without pedalling at all, so the power needed to hold that speed is zero. In reality you would be braking.
- How accurate is the model?
- Martin and colleagues compared it with power measured on the road by a crank-based power meter and found the two closely matched, with a standard error of 2.7 watts, using drag areas measured in a wind tunnel for each rider. With estimated inputs, the answer is only as good as the estimates.