Where your watts go
When you ride a bike, your legs push against three forces. Air resistance grows with the square of your airspeed and dominates on the flat above about 12 mph. Rolling resistance comes from tires deforming on the road and changes little with speed. Gravity only matters on slopes, but on a climb it quickly becomes the largest of the three. This calculator adds them up and tells you how many watts you need to hold a given speed.
The formulas
- Rolling: F = Crr × m × g × cos(θ)
- Gravity: F = m × g × sin(θ), with θ = arctan(grade)
- Air: F = ½ × ρ × CdA × (speed + headwind)², with ρ = 1.225 kg/m³ at sea level
- Power = total force × speed ÷ 0.975, the last term for about 2.5% drivetrain loss
- Calories per hour ≈ watts × 3.6 ÷ 4.184 ÷ 0.24, assuming 24% muscle efficiency
m is the total mass of rider and bike, Crr the rolling coefficient and CdA the drag area, which depends on your position.
Worked example
A 170 lb rider on a 20 lb road bike rides at 18 mph on a flat road, hands on the hoods (CdA 0.40), with standard tires (Crr 0.005).
- Air: about 128 W, three quarters of the effort.
- Rolling: about 34 W.
- Total with drivetrain loss: 166 W, or 2.15 W/kg.
- That costs roughly 590 calories per hour.
A 10 mph headwind pushes the same speed to about 350 W. On a 6% climb at 10 mph, gravity alone takes about 226 W and the total is around 275 W.
Position makes a big difference
Same rider, 18 mph, flat road:
| Position | CdA (m²) | Power needed |
|---|---|---|
| Upright, city or hybrid bike | 0.55 | 215 W |
| Road bike, hands on the hoods | 0.40 | 166 W |
| Road bike, hands in the drops | 0.32 | 140 W |
| Aero bars or time trial | 0.25 | 117 W |
What the numbers mean
- Power-to-weight decides climbing speed. Recreational riders often sustain 2 to 2.5 W/kg for an hour, regular club riders 3 to 4 W/kg, professionals 5 to 6 W/kg.
- Drafting behind another rider can cut air resistance by 25 to 40%.
- Lighter bikes matter on climbs, not much on the flat, where aerodynamics wins.
- Accuracy: expect 10% or more of difference from a power meter. Tire pressure, clothing, road surface and air density at altitude all shift the result.