Calculator
One set of numbers for you and your bike, then what it means: what you can climb, how fast you go for a given power, where that power actually goes, and what to run in your tyres.
Your setup
Rider and bike
Position and surface
Conditions
Gearing
What you can climb
At your sustainable power, on each gradient: the speed you settle at, and whether your lowest gear will still turn at a cadence you can hold. Where it will not, the gear has run out before your legs have — you need a bigger cog, not more power.
| Gradient | Speed | Time / km | Lowest gear | Cadence there | Verdict |
|---|
How long you can hold it
Where your lowest gear forces you above threshold, the climb becomes a countdown. This is how far up it you get before the tank is empty — at your sustainable power the answer is "as long as your legs and your food last", and above it the clock starts. The model behind it only means much between roughly two and forty minutes: barely over threshold it divides by almost nothing and predicts hours, which is arithmetic rather than physiology, so anything past forty minutes is shown as exactly that and no further.
| Gradient | Power it takes | Of threshold | You last | Which gets you | Climbing |
|---|
Where the power goes
The same watts fight different things at different speeds. On the flat, drag grows with the cube of speed, so the top end is almost all air — which is why position beats fitness there, and why it barely matters going uphill.
The top end
Spin-out is where your biggest gear runs out of cadence — past that you can only coast. Terminal speed is what gravity alone would give you on a straight, open descent with no pedalling and no braking, which is where drag rather than gearing sets the limit. It is what the physics says, not a target: real descents have corners, surfaces and other traffic.
| Descent | Coasting speed | Still pedalling? |
|---|
What actually buys you speed
Each change on its own, from where you are now. The usual answer is that position is cheap and weight is expensive — but on a steep enough climb that flips, which is the whole argument in one table.
| Change | Flat speed | Per 10 km | At 6% | Per 1 km of it |
|---|
A climb in particular
Tyre pressure
A starting point, not a rule. It comes from the standard 15% tyre-drop guidance, adjusted down for rough ground and for tubeless. Rolling resistance is fairly flat either side of the ideal and then rises sharply once a tyre is too hard for the surface, so if in doubt go lower — and never exceed what the tyre or rim is rated for.
Gearing
Speed range per gearbars span your low to high cadence
Step between gears
The jump at each shift. Under about 10% feels smooth; much over 15% and the cadence drop is obvious every time.
Every combination
| Front | Rear | Ratio | Gear inches | Development | Gain ratio | Speed |
|---|
How it is worked out
All standard: the power model is the one Gribble and Martin et al. use, the gain ratio is Sheldon Brown's, and the pressure fit is anchored to published tyre-drop tables.
Wheel and gearing
Gear inches G, development D, gain ratio γ. Only the gain ratio knows about crank length L, which is why two riders on the same gear inches are not always pushing the same gear.
Air density
Thinner air at altitude cuts drag and costs nothing — the one free speed there is. h elevation, T absolute temperature.
The three forces
Gravity and rolling both scale with weight; drag does not care what you weigh, only how big you are and how fast you are going. θ is the road angle, vw the headwind.
Power
Force times speed, divided by drivetrain efficiency η — about 97.6% for a clean chain. Because the drag term already carries v², aerodynamic power goes with v³: going 10% faster on the flat costs about a third more power.
Going the other way, from power to speed, there is no clean rearrangement — it is a cubic. This page solves it by bisection, which is exact enough to the nearest 0.01 km/h.
Can you turn the gear?
Your lowest gear at the slowest cadence you can turn sets a floor on speed. If the speed your power gives you on a gradient is below that floor, you cannot ride it seated at a steady cadence however fit you are. That is a gearing problem.
How long above threshold
The critical power model. CP is the power you can hold more or less indefinitely — near enough your threshold — and W′ is the fixed tank of work available above it, usually 15–25 kJ. Ride at P above CP and you empty the tank in t seconds. At or below CP the model says forever, which in practice means food and legs decide, not this equation.
Tyre pressure
A fit to the standard 15% tyre-drop tables: L is the load on that wheel in kg, w the measured width in mm, giving psi. It lands within 3 psi of published guidance from 23 mm to 50 mm. ks takes it down on rough ground, where a tyre that skips loses more than a soft one absorbs, and kt allows the lower pressure tubeless makes safe.