The physics of climbing
Fgravity = 9.81 × mass × sin(θ) · Frolling = 9.81 × mass × cos(θ) × Crr · Fdrag = ½ × CdA × ρ × speed²
θ is the angle of the slope (atan of gradient ÷ 100), mass is rider plus bike, ρ is air density (1.225 kg/m³ at sea level, 15 °C), and drivetrain loss is taken as 2%. This is the standard model used by cycling power calculators such as gribble.org’s. On steep climbs gravity dominates; on shallow ones air drag matters more.
Power needed by gradient and speed
For an 80 kg rider + bike on the hoods (CdA 0.32, Crr 0.005):
| Speed | 4% | 6% | 8% | 10% | 12% |
|---|---|---|---|---|---|
| 8 km/h | 82 W | 118 W | 153 W | 188 W | 223 W |
| 10 km/h | 104 W | 149 W | 193 W | 237 W | 280 W |
| 12 km/h | 127 W | 181 W | 234 W | 286 W | 339 W |
| 15 km/h | 164 W | 231 W | 297 W | 363 W | 428 W |
| 18 km/h | 205 W | 285 W | 364 W | 443 W | 522 W |
| 22 km/h | 266 W | 363 W | 460 W | 557 W | 653 W |
How much does weight matter?
On a steep climb the power needed is almost proportional to total mass. Losing 1 kg from an 80 kg rider-and-bike system saves a little over 1% of the power at the same speed — or about 1% of the time at the same power. On an hour-long climb that is about 40 seconds.
Typical values. The CdA and Crr figures are typical values, not measurements of you. Wind, road surface and drafting change real-world results; on climbs steeper than about 6% their effect is small.
Last reviewed: 2026-10-04 · Disclaimer