What the inputs mean
- Speed, grade and headwind: the ride. Grade is rise over run in percent; use negative values for downhill or a tailwind.
- Weights: rider plus bike, bottles and bags. Mass matters for rolling resistance and climbing.
- CdA: drag coefficient times frontal area, in square meters. It depends on your position, clothing and bike.
- Crr: coefficient of rolling resistance, set by the tire, the pressure and the road.
- Air density: 1.225 kg/m³ is the standard atmosphere at sea level and 15 °C.
- Drivetrain efficiency: the share of your pedal power that reaches the rear wheel.
- Ride time and gross efficiency: only for the work and calories. Gross efficiency is the share of the energy your body burns that becomes work at the pedals.
The defaults are example values so the page shows a result. Apart from gross efficiency (see Calories burned below), they are not taken from any study or product. Change them.
The formula
rolling = Crr × m × g × cos(θ)
gravity = m × g × sin(θ), θ = atan(grade ÷ 100)
aero = ½ × ρ × CdA × (v + headwind)²
power at the pedals = (rolling + gravity + aero) × v ÷ efficiencym is rider plus bike in kg, g = 9.80665 m/s², v is ground speed in m/s. For the reverse, the tool finds the speed where this power equals yours, by searching numerically.
Worked example
A 165 lb rider on a 20 lb bike (83.9 kg together) rides 20 mph (8.94 m/s) on flat ground in still air, with CdA 0.32, Crr 0.005, air at 1.225 kg/m³ and 97% efficiency.
- Rolling: 0.005 × 83.9 × 9.807 = 4.11 N, × 8.94 m/s = 36.8 W
- Aero: ½ × 1.225 × 0.32 × 8.94² = 15.67 N, × 8.94 = 140.1 W
- At the wheel 176.9 W, at the pedals 176.9 ÷ 0.97 = 182 W
Air drag takes 76.8% of the total, rolling 20.2% and the drivetrain 3.0%. Air drag grows with the cube of speed, so at 25 mph the same rider needs 329 W. Going the other way, 250 W gives about 22.6 mph (36.3 km/h).
Calories burned
Add a ride time and the tool turns the power into work, then into food calories:
work (kJ) = power at the pedals (W) × time (s) ÷ 1,000
calories (kcal) = work (kJ) ÷ 4.184 ÷ gross efficiency4.184 kJ is one kcal. Gross efficiency is the share of the energy your body burns that becomes work at the pedals. We use 20%: a 2019 study that compared ways of measuring cycling efficiency sums up earlier research as mostly 18 to 20% at 150 W. Source: Matomäki, Linnamo and Kyröläinen (2019), A Comparison of Methodological Approaches to Measuring Cycling Mechanical Efficiency, Sports Medicine Open. It varies between riders and with effort, so enter your own figure if a lab test gave you one.
For the example ride, one hour at 182.3 W is 182.3 × 3,600 ÷ 1,000 = 656.4 kJ of work. 656.4 ÷ 4.184 = 156.9 kcal, and 156.9 ÷ 0.20 = 784 kcal. At 18% it would be 872 kcal. The figure covers steady pedaling at that power only. It is an estimate for exercise, not a diet guide.
Using it
Compare changes one at a time: a lower CdA, a lighter bike on a climb, a headwind. For your number relative to your weight, see the watts per kg calculator. To turn a speed into a gear and cadence, use the bike speed calculator.
Questions
How many watts does it take to ride 20 mph?
With the example values (83.9 kg rider plus bike, CdA 0.32, Crr 0.005, flat, still air), about 182 W at the pedals. CdA changes the answer the most, so enter yours if you know it.
How fast will I go at 200 watts?
With the same example values on flat ground, about 20.7 mph (33.4 km/h). At 300 W it is about 24.1 mph, because air drag rises so quickly with speed.
How much power does a 5% climb take?
At 10 mph on 5% with the example rider, about 226 W at the pedals, and 184 W of it goes into lifting rider and bike. At that point weight matters much more than drag.
How much does a headwind cost?
Riding 20 mph into a 10 mph headwind with the example values takes about 363 W instead of 182 W, because the drag is set by the 30 mph air speed.
How many calories do I burn cycling at 200 watts for an hour?
About 860 kcal. 200 W for 3,600 seconds is 720 kJ of work, or 172.1 kcal; with a gross efficiency of 20% the body burns five times that. At 18% it would be about 956 kcal.