Cycling power, climbing and zones

Fill in the rider and bike, a riding position (which sets CdA, the drag area) and a surface (which sets Crr, the rolling-resistance coefficient), any headwind (negative for a tailwind), altitude and temperature (which set the air density), and the drivetrain efficiency.

Speed & power — either the speed a power gives you, or the power a speed costs, on a given gradient, with where the watts go (air, rolling, climbing, drivetrain) and a chart of speed against gradient at that power (and at ±20%).
Climb — a climb’s distance and either its average gradient or its elevation gain, and the power you will hold: time, speed, VAM (vertical metres per hour), W/kg and the work done. Michele Ferrari’s rule of thumb, W/kg ≈ VAM ÷ (200 + 10 × gradient %), is shown as a cross-check.
Training zones — FTP from a 20-minute test × 0.95 (Allen and Coggan), an 8-minute test × 0.90 (Chris Carmichael), the best minute of a ramp test × 0.75, or typed in; Coggan’s seven power zones in watts and W/kg; and heart-rate zones from your lactate-threshold heart rate (LTHR), Coggan’s five or Joe Friel’s seven. Friel’s LTHR field test: the average heart rate over the last 20 minutes of a 30-minute solo time trial.

The model is the standard one validated by Martin, Milliken, Cobb, McFadden and Coggan ("Validation of a Mathematical Model for Road Cycling Power", Journal of Applied Biomechanics 14, 1998), without the small wheel-bearing and inertia terms:

P = [ m·g·sin θ + Crr·m·g·cos θ + ½·ρ·CdA·(v + v~wind~)² ] · v ÷ η

with θ = atan(gradient), ρ the air density from the ISA barometric formula and the ideal gas law (1.225 kg/m³ at sea level and 15 °C), and η the drivetrain efficiency (about 97–98% for a clean chain). Speed for a power is solved numerically. Energy: kilojoules of work ≈ kilocalories of food, because the body’s gross efficiency (about 20–25%) nearly cancels the 4.184 kJ per kcal.

The positions and surfaces give typical CdA (0.23 on aero bars to 0.55 upright) and Crr (0.0025 on a track to 0.02 off-road) values — orders of magnitude from published wind-tunnel, field and roller tests; your own can differ by 10–20%, so pick Custom if you have measured them. Your units are remembered and shared with the other bike tools.

Limits

Steady state: no acceleration, drafting (which saves 25–40% of the air drag), cornering or braking. Wind is taken as dead ahead or behind.
Climb times assume a steady power and an even gradient; real climbs with steep ramps cost a little more at the same average power.
FTP and zone formulas are conventions for training, not physiology; different coaches use slightly different boundaries. Heart rate lags effort and drifts with heat and fatigue.

Related: gearing calculator (what cadence that speed needs), tyre pressure, maintenance log, spoke length.

Linking to an example

Distances, speeds, weights, heights and temperatures are read in the link’s units: units=metric (kg, km/h, km, m, °C) or units=imperial (lb, mph, mi, ft, °F).

Parameter Meaning Example

Parameter	Meaning	Example
`mode`	`power` (speed from power) or `speed` (power for a speed)	`mode=speed`
`power`, `speed`, `grade`	Speed & power tab: watts, speed, gradient (%)	`power=220&grade=4`
`rider`, `bike`	Rider; bike and kit	`rider=68&bike=8`
`pos`, `cda`	Position: `upright`, `mtb`, `tops`, `hoods`, `drops`, `aero`, or `custom` with `cda` (m²)	`pos=custom&cda=0.26`
`surf`, `crr`	Surface: `track`, `smooth`, `road`, `rough`, `gravel`, `dirt`, or `custom` with `crr`	`surf=gravel`
`wind`, `alt`, `temp`, `eff`	Headwind (negative: tail), altitude, temperature, drivetrain efficiency (%)	`wind=15&alt=1500`
`cdist`, `cby`, `cgrade`, `cgain`, `cpower`	Climb: distance, `grade` or `gain`, gradient (%), elevation gain, power (W)	`cdist=8&cby=gain&cgain=560&cpower=240`
`test`, `tval`	Zones: `20`, `8`, `ramp` or `ftp`, and the result in watts	`test=20&tval=270`
`lthr`, `hrm`	Lactate-threshold heart rate, `coggan` or `friel`	`lthr=162&hrm=friel`
`units`	`metric` or `imperial`	`units=imperial`

mode

power (speed from power) or speed (power for a speed)

mode=speed

power, speed, grade

Speed & power tab: watts, speed, gradient (%)

power=220&grade=4

rider, bike

Rider; bike and kit

rider=68&bike=8

pos, cda

Position: upright, mtb, tops, hoods, drops, aero, or custom with cda (m²)

pos=custom&cda=0.26

surf, crr

Surface: track, smooth, road, rough, gravel, dirt, or custom with crr

surf=gravel

wind, alt, temp, eff

Headwind (negative: tail), altitude, temperature, drivetrain efficiency (%)

wind=15&alt=1500

cdist, cby, cgrade, cgain, cpower

Climb: distance, grade or gain, gradient (%), elevation gain, power (W)

cdist=8&cby=gain&cgain=560&cpower=240

test, tval

Zones: 20, 8, ramp or ftp, and the result in watts

test=20&tval=270

lthr, hrm

Lactate-threshold heart rate, coggan or friel

lthr=162&hrm=friel

units

metric or imperial

units=imperial

Presets (?example=<name>, metric):

example= Shows

`example=`	Shows
`flat-40`	what 40 km/h on the flat costs in the drops
`headwind`	200 W into a 20 km/h headwind
`altitude`	250 W at 2,000 m and 30 °C: thinner air, faster
`alpe-dhuez`	Alpe d’Huez, 13.8 km and 1,071 m, at 250 W
`ventoux-pro`	Mont Ventoux from Bédoin (21.5 km, 1,610 m) at 6 W/kg for a 62 kg rider
`zones-280`	zones from a 295 W 20-minute test (FTP 280 W) and LTHR 168

flat-40

what 40 km/h on the flat costs in the drops

headwind

200 W into a 20 km/h headwind

altitude

250 W at 2,000 m and 30 °C: thinner air, faster

alpe-dhuez

Alpe d’Huez, 13.8 km and 1,071 m, at 250 W

ventoux-pro

Mont Ventoux from Bédoin (21.5 km, 1,610 m) at 6 W/kg for a 62 kg rider

zones-280

zones from a 295 W 20-minute test (FTP 280 W) and LTHR 168

For example ?example=alpe-dhuez or ?mode=speed&speed=35&pos=drops&grade=0.