Cycling Power Calculator Formula

Understand the math behind the cycling power calculator. Each variable explained with a worked example.

Use the Cycling Power Calculator

Formulas Used

Estimated Power

total_power = round(power_aero + power_rolling + power_gravity)

Power-to-Weight

watts_per_kg = round((power_aero + power_rolling + power_gravity) / mass_kg * 100) / 100

Aerodynamic Drag

aero_watts = round(power_aero)

Climbing Power

climbing_watts = round(power_gravity)

Variables

VariableDescriptionDefault
speed_mphSpeed(mph)18
rider_weight_lbsRider + Bike Weight(lbs)185
gradient_percentRoad Gradient(%)0
speed_msDerived value= speed_mph * 0.44704calculated
mass_kgDerived value= rider_weight_lbs * 0.453592calculated
gradient_decimalDerived value= gradient_percent / 100calculated
power_aeroDerived value= 0.5 * 1.225 * 0.32 * 0.88 * pow(speed_ms, 3)calculated
power_rollingDerived value= 0.005 * mass_kg * 9.81 * speed_mscalculated
power_gravityDerived value= mass_kg * 9.81 * gradient_decimal * speed_mscalculated

How It Works

How Cycling Power Is Estimated

Power required to cycle comes from three main sources: aerodynamic drag, rolling resistance, and gravity.

Formula

Total Power = P_aero + P_rolling + P_gravity

  • P_aero = 0.5 x air density x CdA x v^3 (CdA assumed 0.32 x 0.88)
  • P_rolling = Crr x mass x g x v (Crr assumed 0.005)
  • P_gravity = mass x g x gradient x v

    • Where v is speed in m/s, g is 9.81 m/s^2.

    Key Insight

    Aerodynamic drag increases with the cube of speed, so doubling your speed requires roughly 8 times the power to overcome air resistance.

    Worked Example

    Riding at 18 mph on flat road, 185 lbs total rider+bike weight.

    speed_mph = 18rider_weight_lbs = 185gradient_percent = 0
    1. 01Speed = 18 * 0.44704 = 8.05 m/s
    2. 02Mass = 185 * 0.4536 = 83.9 kg
    3. 03P_aero = 0.5 * 1.225 * 0.2816 * 8.05^3 = 90.0 W
    4. 04P_rolling = 0.005 * 83.9 * 9.81 * 8.05 = 33.1 W
    5. 05P_gravity = 0 (flat road)
    6. 06Total = 90 + 33 + 0 = 123 W
    7. 07W/kg = 123 / 83.9 = 1.47 W/kg

    Ready to run the numbers?

    Open Cycling Power Calculator