Hill Climb Power Calculator Formula

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

Use the Hill Climb Power Calculator

Formulas Used

Total Power Required

total_power = round(power_gravity + power_rolling + power_aero)

Power-to-Weight

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

Gravity Component

gravity_pct = round(power_gravity / (power_gravity + power_rolling + power_aero) * 100)

VAM (vertical m/hr)

vam = round(speed_ms * grade * 3600)

Variables

VariableDescriptionDefault
gradient_percentGradient(%)7
speed_mphClimbing Speed(mph)8
total_weight_lbsRider + Bike Weight(lbs)185
mass_kgDerived value= total_weight_lbs * 0.453592calculated
speed_msDerived value= speed_mph * 0.44704calculated
gradeDerived value= gradient_percent / 100calculated
power_gravityDerived value= mass_kg * 9.81 * grade * speed_mscalculated
power_rollingDerived value= 0.005 * mass_kg * 9.81 * speed_mscalculated
power_aeroDerived value= 0.5 * 1.225 * 0.4 * pow(speed_ms, 3)calculated

How It Works

How Hill Climb Power Is Calculated

Climbing requires overcoming gravity plus rolling resistance and aerodynamic drag.

Formula

P_total = P_gravity + P_rolling + P_aero

  • P_gravity = mass x g x gradient x speed
  • P_rolling = Crr x mass x g x speed
  • P_aero = 0.5 x rho x CdA x speed^3

    • On steep climbs (over 5%), gravity dominates and accounts for 80-90% of the power requirement.

    VAM

    VAM (velocita ascensionale media) measures vertical meters gained per hour. Top climbers achieve 1500-1800 m/hr on major climbs.

    Worked Example

    Climbing a 7% gradient at 8 mph, 185 lbs total weight.

    gradient_percent = 7speed_mph = 8total_weight_lbs = 185
    1. 01Mass = 185 * 0.4536 = 83.9 kg
    2. 02Speed = 8 * 0.447 = 3.58 m/s
    3. 03P_gravity = 83.9 * 9.81 * 0.07 * 3.58 = 206 W
    4. 04P_rolling = 0.005 * 83.9 * 9.81 * 3.58 = 14.7 W
    5. 05P_aero = 0.5 * 1.225 * 0.4 * 3.58^3 = 11.2 W
    6. 06Total = 206 + 15 + 11 = 232 W (2.76 W/kg)
    7. 07VAM = 3.58 * 0.07 * 3600 = 902 m/hr

    Ready to run the numbers?

    Open Hill Climb Power Calculator