Loading Cycling Power to Weight…
Rise over horizontal run, the way a road sign writes it.
4 W/kg
Rider mass only, which is the convention. Total mass on the road is 78 kg.
Watts per kilogram is the division. The climbing speed under it is the steady-state power balance validated by Martin, Milliken, Cobb, McFadden and Coggan, “Validation of a Mathematical Model for Road Cycling Power”, Journal of Applied Biomechanics 1998;14(3):276–291, which matched field-measured power with R² = 0.97 and a standard error of 2.7 W. Gravity is taken as 9.80665 m/s².
The model assumes still air, a constant gradient and a speed that is not changing. Real climbs do none of those things: a headwind, a hairpin, a gust off a ridge or a surface that eats watts will all put the road ahead of the arithmetic. Treat the speed as what the physics allows on a smooth, windless, uniform slope, and treat any gap as information about the road rather than about you.
On the flat, raw watts win: air resistance does not care how heavy you are, so the bigger engine goes faster. Point the road upwards and that stops being true, because now every kilogram has to be lifted, and the rider who makes 300 watts at 90 kg is beaten up an alpine pass by one making 250 at 62. Dividing power by mass collapses those two figures into the one number that predicts a climb, which is why teams recruit on it and why riders quote it at each other all winter.
The ratio alone cannot give you a speed. To get one you need total mass on the road including the bike and two full bottles, the gradient, how much energy the tyres bury in the tarmac, how much of the air you have to shove aside, how thick that air is, and how much of your pedalling the chain actually delivers to the rear wheel. The first two are yours. The last four are assumptions, and this tool puts every one of them in an editable box at the bottom rather than hiding them behind a confident-looking answer.
Drag area is the one worth playing with. Sitting up on a 4% drag strip against tucking on the hoods is worth a bicycle-shaped amount of time; on a 10% wall it barely registers, because at nine kilometres an hour there is hardly any air to fight.
Take a 70 kg rider holding 280 watts, on an 8 kg bike with kit and bottles, so 78 kg is going up the hill. On a steady 8% gradient with typical tyres and a normal riding position at sea level, the model settles at about 14.5 km/h, or roughly 1,150 vertical metres an hour. Add twelve kilograms of rider and hold the same 280 watts and the speed drops to about 12.7 km/h, which over a forty-minute climb is more than five minutes.
The tool splits the power at your chosen speed four ways: lifting the mass, rolling the tyres, pushing the air and the small tax the chain takes. On a steep climb the first of those swallows almost everything, which is the physical reason mass dominates and position barely registers. Ease the gradient towards flat and the air term grows until it is the only one that matters.
That split is worth more than the headline speed, because it tells you where an improvement would come from. Somewhere around three to five per cent, depending on the road, the honest answer stops being aerodynamics and becomes either more watts or less rider.
It assumes still air, a gradient that never varies and a speed that never changes. Real climbs are none of those: they ramp and ease, they turn into and out of the wind, and you accelerate out of every hairpin. It also has no opinion about whether you can actually hold that power for the length of the climb, which is the question that decides most rides.
Treat the output as the speed the physics permits on a smooth, windless, uniform slope. When the road gives you something slower, the difference is telling you about the road, the wind or your position rather than about your legs.
The ratio is conventionally quoted against rider mass alone, because that is what makes two athletes comparable, and this tool follows that convention. The climbing speed underneath it uses total mass, because gravity has to lift the bike as well.
Usually wind, a gradient that is steeper in places than its average, or a drag area larger than the default. Enter your own measured drag area and rolling resistance if you have them, and the answer will tighten up considerably.
Vertical ascent metres per hour: the height gained in sixty minutes, ignoring how far you travelled to gain it. Because it strips out the gradient, it lets you compare a shallow twenty-kilometre drag against a short brutal ramp on equal terms.
A kilogram is a kilogram to gravity, so a kilo off the bike and a kilo off the rider climb identically. The bike kilo simply costs a great deal more, and the rider kilo is usually still available.