ABC Tools

Cycling Speed and Power, Explained

After reading this you can predict how fast a given power will push you (or how many watts a target speed demands), and you can see exactly how those watts split between air, road and gravity.

Ride at 200 W on flat, smooth road in the hoods and you travel about 32 km/h. Move the same 200 W to a 6% climb and your speed collapses to roughly 12 km/h. Nothing about your legs changed. The physics changed, because on the flat you are mostly fighting air, and on the climb you are mostly lifting mass against gravity.

The Cycling Speed and Power Calculator solves the standard power equation in both directions. This guide explains that equation term by term, works the demo numbers by hand, and shows where the model is trustworthy and where it is only a rough guide.

What the model does

Cycling power at steady speed balances four things: the air you push aside, the friction of tires on road, the work of raising your combined mass on a grade, and the small tax the drivetrain takes before your legs reach the road. The calculator computes each term from your inputs and either adds them up (to get watts from a speed) or searches for the speed that matches your watts.

The important consequence, and the reason the same watts give wildly different speeds, is that the four terms scale differently. Air resistance grows with the cube of speed. Rolling resistance is nearly flat. Gravity depends only on grade and weight, not on speed at all. Which term dominates depends entirely on how fast and how steep you are going.

When to use it, and when not

Use it to compare positions (how many watts does moving from hoods to drops save at 40 km/h), to set a realistic target speed for a time trial, to estimate a climb pace, or to understand why a headwind hurts so much. The relative answers are reliable even when the absolute number is off, because a wrong CdA shifts every scenario the same way.

The model assumes still air and a steady speed. A real ride has gusts, drafting, corners, and accelerations, none of which appear here. Treat the output as a clean physics baseline, not a promise of the time you will ride.

Do not use it to compare yourself against a friend on a different day and course, or to judge fitness. For that, watts per kilogram is the honest metric. See the Power-to-Weight (W/kg) Calculator.

The formula, term by term

Total power at the rider's legs is the sum of the three resistive powers, divided by drivetrain efficiency:

P = \frac{1}{1 - L}\left( \tfrac{1}{2}\rho\, C_dA\, v^3 + C_{rr}\, m g \cos\theta\, v + m g \sin\theta\, v \right)

Here P is your power in watts, L is the drivetrain loss as a fraction (2.5% is 0.025), \rho is air density in kg/m³, C_dA is drag area in m², v is ground speed in m/s, C_{rr} is the rolling resistance coefficient, m is total mass (rider plus bike) in kg, g = 9.81 m/s², and \theta is the road angle where the grade is \tan\theta.

The three terms inside the bracket are the aero power, the rolling power, and the gravity power. Read them left to right:

Aero
\tfrac{1}{2}\rho\, C_dA\, v^3. Grows with the cube of speed. Double your speed and this term goes up eightfold.
Rolling
C_{rr}\, m g \cos\theta\, v. Grows only linearly with speed. On the flat, \cos\theta \approx 1.
Gravity
m g \sin\theta\, v. Zero on the flat, and it dominates on steep climbs. For small grades, \sin\theta \approx \text{grade}/100.

Air density itself falls with altitude. A common approximation is \rho = 1.225\,(1 - 2.256\times 10^{-5} h)^{4.256}, where h is altitude in metres. At sea level that gives 1.225 kg/m³; at 2000 m it gives about 1.007 kg/m³, roughly 18% less air to push.

Working the demo numbers

200 W on the flat in the hoods

Demo inputs: 200 W, 75 kg rider, 8 kg bike, 0% grade, hoods, smooth asphalt, sea level, 2.5% loss. The hoods preset uses C_dA = 0.32 m² and smooth asphalt uses C_{rr} = 0.005. Total mass is 83 kg. Solve for speed.

  1. Power at the wheel after loss: 200 \times (1 - 0.025) = 195 W.
  2. Try v = 8.9 m/s (32.04 km/h). Aero: 0.5 \times 1.225 \times 0.32 \times 8.9^3 = 138.1 W.
  3. Rolling: 0.005 \times 83 \times 9.81 \times 8.9 = 36.2 W.
  4. Gravity: flat, so 0 W.
  5. Sum at the wheel: 138.1 + 36.2 = 174.3 W. That is short of 195 W, so the true speed is a little higher.
  6. Try v = 9.15 m/s (32.9 km/h). Aero: 0.5 \times 1.225 \times 0.32 \times 9.15^3 = 150.1 W. Rolling: 37.2 W. Sum: 187.3 W. Closer.
  7. Converging near v \approx 9.25 m/s, about 33.3 km/h for the full 195 W.

The calculator does this search for you and lands on the same neighbourhood. The point of the hand version is to show the split: at this speed aero is about four times the rolling term, even before you go fast.

Reading the power split

The most useful output is not the single speed or watt number. It is the breakdown of where your watts go, because that tells you what to change. The table below shows the same 200 W rider (83 kg total, hoods, smooth asphalt) at three grades, holding speed where 195 W of wheel power balances.

Power split for 195 W at the wheel, 83 kg total, hoods, smooth asphalt
GradeSpeed (km/h)Aero (W)Rolling (W)Gravity (W)
0%33.3158380
3%19.63222140
6%12.17.614173

At 6% gravity is about 89% of the load and aero is under 4%. This is why an aero position barely helps on a steep climb, and why losing a kilogram matters far more there than on the flat. The chart makes the crossover visible.

Aero dominates on the flat; gravity dominates on the climb. Rolling is small and steady throughout.

On the flat at 200 W a hoods rider does about 33 km/h with 158 W lost to air and 38 W to the tires. Raise the grade and speed falls fast while gravity takes over: at 6% the same rider does about 12 km/h with 173 W going into the climb.

Common mistakes

The errors that throw the output off the most are usually inputs, not the physics.

  • Guessing CdA too low. The presets are typical values and vary by about ±15% with body size and kit. A rider who assumes 0.25 in the hoods when they really sit at 0.32 will predict a speed several km/h too high.
  • Forgetting the wind. The model assumes still air. A headwind replaces v with (v + w) in the aero term only. A 20 km/h headwind at 30 km/h road speed makes the effective aero speed 50 km/h, and aero power there is more than double.
  • Using rider weight only. The gravity and rolling terms use total mass. Leaving out an 8 kg bike understates climbing power by about 10%.
  • Ignoring altitude. At 2000 m the thinner air cuts aero power by roughly 18%, which is a real free speed on a flat course and a common surprise.

When you compare two scenarios, change one input at a time. If you want the pure aero benefit of the drops, keep power, weight, grade and surface fixed and switch only the position. The speed difference is then attributable to CdA alone.

Related tools

To turn a target speed into the gear and cadence that produce it, use the Bike Gear Ratio Calculator. For the time a specific climb takes at your watts, with VAM, see the Climb Time and VAM Calculator. Rolling resistance depends on inflation, and the Bike Tire Pressure Calculator gives sensible starting pressures. If your position feels wrong, the Bike Frame Size Calculator checks fit from height and inseam, and rowers can convert efforts with the Rowing Split to Watts Converter.

Frequently asked questions

Why does 200 W give 33 km/h on the flat but only 12 km/h on a 6% climb?

On the flat you spend nearly all your watts on air resistance, which grows with the cube of speed, so a lot of watts buys only a little more speed. On the climb almost all your watts go into lifting 83 kg against gravity, and that term is proportional to speed, so power buys speed much more slowly and the number lands lower.

How accurate is the predicted speed?

The physics is exact for the inputs you give. The uncertainty lives in CdA (about ±15%) and Crr. Because aero power scales with CdA directly, a 15% CdA error moves flat-road speed by roughly 4 to 5%, so treat a 33 km/h prediction as roughly 31 to 35 km/h.

Does a lighter bike make me faster on the flat?

Barely. On the flat, weight enters only the rolling term. Dropping 1 kg off 83 kg cuts rolling power by about 0.45 W at 33 km/h, worth a fraction of a km/h. On a 6% climb the same kilogram is worth about 2 W, which is real time.

How do I add a headwind?

This tool assumes still air, so it has no wind field. Approximate a headwind by raising your speed input in the aero term mentally: a 15 km/h headwind at 30 km/h behaves like riding into still air at 45 km/h for the drag calculation, which roughly doubles the aero watts.

What drivetrain loss should I use?

A clean, well-lubricated chain loses about 2 to 3%. A dry or dirty chain can lose 4% or more. The default of 2.5% is a fair figure for a maintained road drivetrain.

Try it yourself in the tool

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