The three terms, and how their shares move
Total power at the wheel is the sum of three things. Gravity takes mass times 9.8067 times speed times the sine of the road angle. Rolling resistance takes a coefficient times mass times gravity times the cosine of that angle times speed. Aerodynamic drag takes half the air density times the drag area times speed cubed. Divide the sum by drivetrain efficiency and you have what the legs must produce.
The interesting part is not the formula but how the shares shift. Two of the terms are linear in speed and the third is cubic, so as speed rises the air term takes over everything. Run a 75 kilogram system up a five kilometre climb at eight percent in 25 minutes and gravity takes about 196 watts, rolling about 12, and air about 8 — roughly 91, 6 and 4 percent. Take the same system along a nearly flat five kilometres in ten minutes and the split flips to about 31 watts gravity, 31 rolling and 124 air, with air taking two thirds of the total.
That single reversal explains most of the received wisdom in cycling. Weight obsession is rational on steep climbs and close to pointless on flat ground. Aerodynamic equipment is transformative on the flat and marginal on a mountain pass. Drafting saves a third of your power in a fast bunch and almost nothing at eight kilometres an hour up a wall.
Reading the climbing rate
Vertical ascent per hour is the number that compares climbs fairly, because it strips out length and gradient and leaves the rate at which you gain height. A rider doing 400 metres of gain in 25 minutes is climbing at about 960 metres an hour, and that figure means the same thing on a short steep ramp and a long alpine pass.
| Climbing rate | Roughly what it takes on a moderate climb |
|---|---|
| 500 to 700 m/hour | A steady recreational effort, conversation just about possible |
| 700 to 900 m/hour | A firm tempo you could hold for a long climb |
| 900 to 1,200 m/hour | Threshold territory for most trained amateurs |
| Above 1,400 m/hour | The territory of professional racing, sustained only briefly by anyone else |
The bands are orientation rather than targets, and they move with the rider mass. Climbing rate is close to a direct restatement of watts per kilogram on steep ground, which is why the two numbers track each other so tightly and why neither means much on the flat.
The inputs you should be suspicious of
Mass you can weigh, gradient you can read from a map, distance you can measure. The other three are estimates and they deserve different amounts of trust.
Rolling resistance is the most stable. The coefficient for a decent road tyre on ordinary tarmac sits near 0.005 and the practical range across sensible equipment is maybe half to double that. It contributes a few percent on a climb, so a large error here changes the answer very little.
Drag area is the least stable. It depends on your height and build, your position, what you are wearing and how still you hold it, and a rider picking from a list can be twenty percent out without doing anything unreasonable. On an eight percent climb that error is worth a watt or two. On flat ground it is worth twenty, which is why any power estimate for a flat ride should be treated as a rough bracket rather than a figure.
Air density is small but not negligible at altitude. At 2,000 metres it is about eighteen percent lower than at sea level, which cuts the aerodynamic term by the same proportion. That is a real gain on a fast descent and irrelevant on the climb that got you up there, where the thinner air also means less oxygen and the net effect on a rider is firmly negative.
Why the average gradient understates a real climb
The model treats the climb as one constant slope, and no climb is. Power required rises faster than linearly with gradient at constant speed, so a road that alternates between four percent and twelve percent costs more power to ride at a given average speed than a uniform eight percent road does. A rider holding constant power instead will be slower on the steep pitches and faster on the shallow ones, and the time lost to the former outweighs the time gained by the latter.
The practical consequence is that a computed time for a climb with a lumpy profile is optimistic, sometimes by several percent. If the climb has ramps into the mid teens, break it into sections and run each one, or accept that the single-figure answer is a floor rather than a forecast.
Turning a power figure into a plan
A watt figure only means something against your own capacity, which is where the power zones calculator comes in: a climb that demands 105 percent of your threshold for forty minutes is not a pacing question, it is an arithmetic impossibility, and knowing that before the start is worth more than any equipment choice. Gearing is the other half of the same problem, because holding a workable cadence at a low speed requires a low enough gear, and the bike gear ratio calculator shows whether the bottom gear you own can do it. For rides where the climb is one part of a longer day, the average speed and calorie side sits in the cycling speed calculator, and fluid loss on a long hot climb is worth checking against the sweat rate calculator.
Questions people ask
Why is the power figure higher than my power meter shows on the same climb?
Several reasons stack in the same direction. The model assumes a constant gradient, and a real climb with steeper pitches costs more than its average implies. It assumes still air, and even a light headwind adds meaningfully at low speed. It uses the drag area you selected rather than yours. And drivetrain efficiency at low cadence in a cross-chained gear is worse than the default. Going the other way, a power meter measures at the crank or pedal and may read a few percent low or high against its own specification. If the gap is under about five percent, the model is behaving; if it is twenty percent, check the gradient figure first, since map elevation data is often the largest single error.
Does weight really matter that much on a climb?
On a steep climb, close to proportionally. The gravity term is directly proportional to total mass, and it is around ninety percent of the total at eight percent gradient, so removing one percent of system mass cuts the required power by roughly nine tenths of a percent at the same speed, or gains you about that much speed at the same power. For a 81 kilogram rider and bike, one kilogram is about 1.2 percent, which is around fifteen seconds on a 25 minute climb. That is a real but modest amount, and it is why the honest comparison is against everything else a kilogram of equipment cost you. On flat ground the same kilogram is worth almost nothing.
How much does drafting help on a climb?
Much less than on the flat, and by an amount that falls away as the gradient rises. Drafting reduces the aerodynamic term, which at eight percent is only a few percent of the total, so even a large proportional saving on a small share is a small number. At the speeds of a fast flat bunch the same shelter can cut total power by a quarter or more, because there the air term is most of the work. This is the physical reason climbs break groups apart and flat sections hold them together, independent of anything about who is stronger.
What is the difference between gradient as a percentage and as an angle?
Percentage gradient is rise divided by horizontal run, expressed as a percentage, and the angle is the arctangent of that ratio. At small gradients the two are almost interchangeable: 8 percent is 4.57 degrees, and the sine and the raw ratio differ by about a third of a percent. The gap widens as the road steepens, and at 20 percent using the ratio directly rather than its sine overstates the gravity term by about two percent. This calculator converts properly, which matters mainly if you are working with genuinely steep ground. A separate trap is that some sources compute gradient against distance along the road rather than the horizontal, which is a different and slightly smaller number.
Can I use this for an e-bike?
The physics is identical, but two of the inputs change and one output means something different. Add the motor and battery to the bike weight, which is often an extra fifteen to twenty-five kilograms on a heavier machine, and that mass goes into the gravity term like any other. The power figure the calculator produces is then the total at the rear wheel, which is the sum of what you contribute and what the motor contributes, so it does not tell you what your legs are doing unless you know the split. Nothing here describes what any particular class of assisted bicycle is permitted to do on the road, which varies by jurisdiction and is not a question a calculator can answer.