Climbing power calculator

This calculator takes body weight in kilograms, net vertical gain in metres, and a strictly positive time in seconds, multiplies mass by 9.80665 m/s² and by height to form work in joules, divides by time to form power in watts, and returns structured JSON with work_joules, power_watts, vertical_speed, the gravity constant used, formula, and method. Zero time, negative time, non-positive mass, negative gain, missing fields, and non-finite values fail with invalid_input before any result is returned.

What climbing power means and which three quantities you need to send

Delivering body_weight, vertical_gain, time, g, work_joules, power_watts, vertical_speed, formula, and method as JSON makes the result easy to paste into training notes, diff in automated tests, or reuse across languages without reimplementing the arithmetic. This model reports pure mechanical power against gravity only; it does not add horizontal walking cost, pack inefficiency, air drag, or metabolic conversion factors.

How this calculator validates input and applies P = m · g · h / t

Numeric strings that parse to finite numbers are accepted so forms and CSV-style pipelines can pass values without an extra cast. Body weight must be strictly positive because zero or negative mass has no physical meaning for gravitational work. Vertical gain must be non-negative; pure descent is outside this ascent-power model. Time must be strictly positive; zero duration is rejected with a clear message because power is undefined when you divide by zero in this average-power model, and negative time is likewise refused. There is no variable grade profile, no efficiency correction, and no unit auto-conversion; this is ideal average mechanical climbing power from the three known quantities. Send a JSON body with body_weight, vertical_gain, and time. All three fields are required and must be finite: missing any field, empty strings, non-numeric text, NaN, and Infinity all fail immediately with invalid_input before any result is returned, and failed validation is not charged. Aliases are recognized for convenience: body_weight also accepts mass, m, weight_kg, and body_mass; vertical_gain also accepts height, h, elevation_gain, and gain_m; time also accepts t, duration, and time_s. After validation, work_joules is body_weight times g times vertical_gain with g fixed at 9.80665, power_watts is work_joules divided by time, and vertical_speed is vertical_gain divided by time. Results are rounded to a stable decimal precision so the same input always yields the same JSON across JavaScript engines. The same pure function powers the free in-browser tool and the API path.

Practical use, limits, pricing, and delivery channels

Use the browser tool when you want an immediate watts check after a summit push, a stair-climb interval, a treadmill incline session with known elevation, or a homework problem that states mass, height, and time. There is no language model, no external physics service, and no randomness, so the capacity is safe to pin in continuous-integration checks and reproducible lesson materials. Each successful request is one billable item at $0.002; failed validation does not consume balance. Choose SI units consistently—if body weight is in kilograms, vertical gain in metres, and time in seconds, power_watts is true SI watts and vertical_speed is metres per second. Results are fully deterministic: the same mass, gain, and time always yield the same work_joules and the same power_watts. Wire the endpoint into hike analytics, contest answer checkers, coach dashboards, or preprocessing steps where you already prefer explicit domain errors—such as rejecting zero time—over opaque black-box widgets that cannot explain why a bad input was refused. Remember the model is mechanical only: metabolic cost and pack factors require separate adjustments outside this endpoint.