Cycling speed is the one number here that needs no model at all: distance divided by time, and nothing else comes into it. Ride 40 kilometres in 1:20:00 and you averaged 30.00 km/h, or 18.64 mph, which is 2:00 per kilometre and 3:13 per mile. That part is arithmetic and this page gives it to you as ...
These do not change your speed — that comes from distance and time. They decide what that speed cost you.
Negative gradient is a descent; negative headwind is a tailwind. Air density here is 1.2250 kg/m³.
AVERAGE SPEED
30.00 km/h
18.64 mph · 8.333 m/s
PER KM
2:00
PER MILE
3:13
POWER
152 W
2.02 W/kg
WORK
727 kJ
at the pedals
ENERGY
724 kcal
burned by you
What it costs to hold each speed, for your rider and conditions. The bands stack in order — rolling, air, gradient, drivetrain — so the top of the stack is what your legs put in. The full-height dashed line with the dot marks your 30.00 km/h. The short tick on the axis is 16.5 km/h, where air overtakes rolling resistance. Both axes are linear.
| What is resisting you | Force | Power | Share of the total |
|---|---|---|---|
| Rolling resistance | 4.12 N | 34.3 W | 22.7% |
| Air resistance | 13.61 N | 113 W | 74.8% |
| Gradient | 0.00 N | 0.00 W | 0.0% |
| Drivetrain loss | — | 3.79 W | 2.5% |
| At the pedals | 17.73 N | 152 W | 100.0% |
Force times speed is power, so each row is simply its force multiplied by 8.333 m/s. Drivetrain loss has no force of its own — it is the 2.5% of your input the chain and bearings absorb before it reaches the road. A negative row is helping rather than resisting.
Each row changes exactly one thing and re-solves for the speed the same 152 W would give you, on your 0.0% gradient. The ranking is not fixed — it moves with the gradient, which is the whole point.
| Change one thing | New speed | Difference |
|---|---|---|
| Nothing — as you rode it | 30.00 km/h | — |
| Ride 10% harder | 31.14 km/h | +1.14 |
| Tuck lower (CdA −0.03) | 30.91 km/h | +0.91 |
| Faster tyres (Crr −0.001) | 30.55 km/h | +0.55 |
| Lose 5 kg of rider | 30.16 km/h | +0.16 |
| 10 km/h headwind | 24.29 km/h | -5.71 |
| 10 km/h tailwind | 36.36 km/h | +6.36 |
The same rider and conditions across a range of speeds. Watch the last column: air resistance takes over early and then takes almost everything.
| Speed | Pedal power | Air’s share of your power |
|---|---|---|
| 15 km/h | 32.1 W | 44.1% |
| 20 km/h | 57.9 W | 58.0% |
| 25 km/h | 96.7 W | 67.9% |
| 30 km/h | 152 W | 74.8% |
| 35 km/h | 226 W | 79.8% |
| 40 km/h | 323 W | 83.3% |
| 45 km/h | 445 W | 85.9% |
| 50 km/h | 597 W | 87.9% |
Forty kilometres in 1 hour 20 minutes, a 75 kg rider on a 9 kg bike, flat road at sea level and 15 degrees, hands on the hoods (CdA 0.32) on ordinary asphalt (Crr 0.005). Speed first, which needs no physics: 40,000 m divided by 4,800 s is 8.333 m/s, or 30.00 km/h and 18.64 mph. That is 2:00 per kilometre. Now what it cost. Total mass is 84 kg and air density at sea level and 15 degrees is 1.2250 kg/m3. Rolling: 0.005 x 84 x 9.80665 = 4.12 N, which at 8.333 m/s is 34.3 W. Air: 0.5 x 1.2250 x 0.32 x 8.333 squared = 13.61 N, which is 113 W. Gradient: zero, the road is flat. That is 147.7 W at the wheel. Dividing by 97.5% drivetrain efficiency gives 152 W at the pedals, of which 3.79 W is lost in the chain. Air is taking 74.8% of the total, and it passed rolling resistance as the larger cost back at 16.5 km/h. Over 4,800 seconds, 152 W is 727 kJ of work, and at 24% gross efficiency that is roughly 724 kcal burned.
Speed itself is the easy part: distance divided by time, and nothing else enters into it. What takes explaining is why a particular speed is hard, and that comes down to three forces the bike has to overcome, plus a small tax on the way through the chain.
speed = distance ÷ time
rolling = Crr · m · g · cos θ
air = ½ · ρ · CdA · (v + wind)²
gradient = m · g · sin θ
power = (rolling + air + gradient) · v ÷ 0.975
The important detail is the exponent. Rolling resistance and gradient are both flat forces, so their power cost rises in step with speed — go twice as fast and you pay twice as much. Air resistance is a force that already grows with the square of speed, and power is force times speed, so its cost grows with the cube. That single difference is why cycling rewards aerodynamics so much more than it rewards strength, and why the gap widens the faster you go.
For your numbers, air resistance overtakes rolling resistance at roughly 16.5 km/h. Below that the road is your main opponent; above it, the air is — and it only gets more so. Note that θ is the angle of the slope, not the percentage: a 10% gradient is atan(0.10) = 5.71°, and using 0.10 directly for sin θ would overstate the climbing force by about half a percent.
Last updated: July 29, 2026 · Formula verified · Speed is exact; power is a physical model, and CdA and Crr are the two figures worth measuring rather than guessing · Eagle-eyed accuracy for every calculation.