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09 Cycling and Outdoors

Bike Climbing Power Calculator

Card No. 09·0038 · Updated · Standard formula, shown below

Power needed 230 W
Power per kg of rider
3.28 W/kg
Result
Climbing rate (VAM)
898 m/h
Result
Of which lifting against gravity
196 W
Result
You enter
Rider weight, Bike and kit weight, Gradient, Speed
You get
Power needed, Power per kg of rider, Climbing rate (VAM), Of which lifting against gravity
Rounding
0 dp · 2 dp

This calculator estimates the power a cyclist needs to climb a hill at a steady speed. Enter rider and bike weight, the gradient and the speed; you get total power in watts, watts per kilogram of rider and the vertical climbing rate (VAM).

Formula

P = v × (m g (sin θ + Crr cos θ) + ½ ρ CdA v²), with θ = arctan(gradient ÷ 100) and v in m/s (km/h ÷ 3.6). Fixed values: rolling resistance Crr = 0.005 (good road tyres), air density ρ = 1.225 kg/m³, drag area CdA = 0.4 m² (upright on the hoods). VAM = v × sin θ × 3600.

  • m: rider + bike mass, kg; g = 9.80665 m/s²
  • gradient: rise per 100 m of road, %

Worked Example

70 kg rider, 10 kg bike, 6% at 15 km/h.

  1. v = 15 ÷ 3.6 = 4.1667 m/s; θ = arctan(0.06) = 3.434°
  2. Gravity: 80 × 9.80665 × 0.059892 × 4.1667 = 196 W
  3. Rolling: 80 × 9.80665 × 0.005 × 0.998205 × 4.1667 = 16.3 W; air: 0.5 × 1.225 × 0.4 × 4.1667³ = 17.7 W
  4. Total = 196 + 16.3 + 17.7 = 230 W; 230 ÷ 70 = 3.28 W/kg
  5. VAM = 4.1667 × 0.059892 × 3600 = 898 m/h

Limits and common mistakes

  • It ignores drivetrain loss (about 2-4%) and wind, so a power meter will read a little higher.
  • On steep climbs gravity dominates; on the flat, air drag does.
  • Gradient on signs is often the maximum, not the average of the climb.
Formula used
in rm | Rider weight | kg | 70 | 0 | 300
in bm | Bike and kit weight | kg | 10 | 0 | 100
in g | Gradient | % | 6 | 0 | 40
in v | Speed | km/h | 15 | 0 | 100
out p | Power needed | W | (v / 3.6) * ((rm + bm) * 9.80665 * (sin(atan(g / 100)) + 0.005 * cos(atan(g / 100))) + 0.5 * 1.225 * 0.4 * (v / 3.6)^2) | 0
out wkg | Power per kg of rider | W/kg | p / rm | 2
out vam | Climbing rate (VAM) | m/h | (v / 3.6) * sin(atan(g / 100)) * 3600 | 0
out pg | Of which lifting against gravity | W | (rm + bm) * 9.80665 * sin(atan(g / 100)) * (v / 3.6) | 0

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Photo collage: a cyclist from behind riding up a steep mountain road switchback, and a close-up of the bike crank.
Save this card: a 1000 × 1500 image of Bike Climbing Power Calculator.

Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.

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