The bicycle power calculator and the vertical speed calculator both quantify climbing, but from opposite sides. Bicycle power estimates the watts a given speed, grade, wind, and body position require — the effort side of the climb. Vertical speed reports how quickly you gain or lose height from a signed distance and elapsed time — the outcome side. One needs a long list of scenario coefficients; the other needs just two numbers.
What each calculator does
The bicycle power calculator takes mass, rolling-resistance coefficient, grade, ground speed, wind speed, drag area (CdA), air density, and drivetrain efficiency. Rolling force is the coefficient times mass times 9.80665; grade force is mass times 9.80665 times grade divided by 100; aerodynamic force is half times density times CdA times the square of the relative air speed. Wheel power is total force times ground speed, and input power divides wheel power by the entered efficiency. In the page’s worked example — 75 kg, a 2 percent grade, 10 m/s ground speed, a 2 m/s headwind — the components sum to about 46 N and input power is about 461.3 W, displayed to one decimal. The page stresses that results are sensitivity arithmetic, not performance or fitness guidance.
The vertical speed calculator takes a signed vertical distance and elapsed minutes and seconds. It converts the distance exactly — the international foot is defined as exactly 0.3048 meter per NIST Special Publication 811 — divides by the raw elapsed time, and reports neutral per-second, per-minute, and per-hour rates. Positive and negative values indicate direction only, no aircraft or hiking inference is made, and a nonzero rate whose supported fixed-precision values would all round to zero is reported as too small to display rather than as a zero result. Zero elapsed time triggers a validation message instead of a result.
Side-by-side
| Bicycle power calculator | Vertical speed calculator | |
|---|---|---|
| Inputs | Mass, rolling resistance, grade, speed, wind, CdA, air density, efficiency | Signed vertical distance, elapsed minutes and seconds |
| Primary output | Input power in watts, one decimal | Neutral ascent or descent rates per second, per minute, and per hour |
| What the number means | Mechanical power the entered scenario requires | Vertical change per unit time; direction only |
| Formula basis | Rolling + grade + aero forces, summed, times ground speed, divided by efficiency | Signed distance divided by raw elapsed time, with exact foot-to-meter conversion |
| Example | 75 kg, 2% grade, 10 m/s, 2 m/s headwind → about 461.3 W | Distance and time entered directly; no mass or resistance inputs |
| Effort versus outcome | Effort side of a climb | Outcome side of a climb |
| Caveats | Sensitivity arithmetic, not performance advice | No aircraft, hiking, or personal-performance inference |
When to use which
Use the bicycle power calculator when your question is about effort: how many watts a given speed on a given grade with a given wind will require, or how the components — rolling, grade, and aerodynamic drag — divide up. It is the tool for gear and pacing planning, and its page points to the bicycle gear, gear ratio, and cadence calculators for the gearing context around a measured scenario.
Use the vertical speed calculator when your question is about the rate of height change itself: how fast a climb or descent proceeds from an elevation gain and a time, without any assumption about what is doing the climbing. It needs only distance and time, and its page points to the speed, feet-per-second, and m/s-to-km/h converters for speed-unit conversions around the rates.
For a cyclist, the two complement each other: watts describe what the climb demands, while vertical speed describes how quickly the elevation is being won. Neither page makes a performance judgment — the power result is explicitly sensitivity arithmetic, and vertical speed explicitly makes no personal-performance inference.
Limits and disclaimer
The bicycle power calculator is scenario arithmetic built from the coefficients and measurements you enter; the uncertainty of those factors must be supplied, and the result is not performance, fitness, training, equipment, or safety guidance. The vertical speed calculator is neutral distance-over-time arithmetic: terrain, horizontal distance, pauses, measurement error, aircraft performance, and personal capability are outside the calculation, and direction only reflects sign. Both pages retain full precision until the labeled display step, reject invalid inputs rather than showing misleading results, and are educational tools rather than instruments for training prescriptions or performance claims.