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

    Frequently Asked Questions

    What is a good watts per kg for cycling?

    Recreational: 1.5-2.5 W/kg, competitive amateur: 3-4 W/kg, professional: 5-7 W/kg at threshold.

    Why does power increase so much at higher speeds?

    Aerodynamic drag grows with the cube of speed. Going from 15 to 20 mph requires roughly twice the power, even on flat ground.

    How accurate is this estimate?

    This provides a reasonable estimate assuming standard road conditions. Real power depends on wind, drafting, road surface, tire pressure, and rider position.

    Ready to run the numbers?

    Open Cycling Power Calculator