HesapHanem

Cycling Power Calculator

Find the watts required for your cycling speed and gradient.

How it is calculated

The speed is converted to v = km/h / 3.6 (m/s). Three forces resist the rider: gravity Fg = m·g·sin θ, rolling resistance Fr = Crr·m·g·cos θ and air drag Fa = ½·ρ·CdA·v². The gradient is a percentage, with θ = atan(grade / 100). Power at the wheel is (Fg + Fr + Fa) × v and is divided by 0.97 for drivetrain losses to get the rider's power in watts.

The tool uses g = 9.81 m/s² and air density ρ = 1.225 kg/m³ (sea level, 15 °C). Mass is rider plus bike in kg. If CdA or Crr are empty or zero, defaults of 0.32 m² and 0.005 are used, and grade defaults to 0. There is no wind. On a steep descent the result can come out negative, meaning no pedalling is needed.

Worked example

An 80 kg rider and bike climb an 8% grade at 15 km/h. v = 15 / 3.6 = 4.167 m/s and θ = atan(0.08) = 4.57°. Gravity: 80 × 9.81 × sin θ = 62.6 N. Rolling: 0.005 × 80 × 9.81 × cos θ = 3.9 N. Air drag: 0.5 × 1.225 × 0.32 × 4.167² = 3.4 N. Total 69.9 N, times 4.167 m/s is 291 W, divided by 0.97 gives 300 W. Per kilogram, that is 3.75 W/kg.

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Common mistakes

  • Entering rider weight only: the weight field should be rider plus bike (and bottles, bag), because the engine uses it as total mass.
  • Typing the grade as a decimal fraction (0.08 instead of 8): it is a percentage, so 0.08 means a nearly flat road.
  • Using climbing results for flat riding, or the other way round: on a climb gravity dominates, but at 30 km/h on the flat most of the power (about three quarters with the default settings) goes into air drag.
  • Comparing the answer with a power meter reading in the wind: the estimate assumes still air and sea-level density, so headwind, altitude and drafting change the real figure.

About this calculator

This calculator estimates the power (watts) a cyclist must produce to hold a given speed, by summing the three main resistive forces: rolling resistance (from tire/road friction and rider+bike weight), gravity (from the road gradient), and aerodynamic drag (proportional to the square of speed, scaled by frontal area and drag coefficient CdA).

Cyclists and coaches use it to translate a target speed or finish time into a required power output for pacing a climb or time trial, to compare how much extra power steep gradients demand, and to see how much aerodynamic position (lower CdA) or lighter equipment can save.

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Comments (1)

  • Editorial team

    Air drag grows with the cube of speed in power terms, so the last few km/h on the flat are costly. With the default settings and an 80 kg rider and bike, 30 km/h takes about 151 W and 35 km/h about 225 W, roughly half as much power again for a 17% speed gain. Remember there is no wind or drafting here. What speed and power figures do you compare it with from your own rides?

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