# Vertical Jump Power Calculator

> Estimates lower-body power from a vertical jump height and body mass with the Sayers peak-power equation (60.7·height + 45.3·mass − 2055), the Harman peak-power equation and the Lewis average-power formula, plus take-off velocity and flight time.

- Calculator id: `vertical-jump-power` · Category: Sports & Fitness (`fitness`) · Tool name: `estimate_vertical_jump_power`
- Canonical page: https://tttkmbb.com/fitness/vertical-jump-power · This document: https://tttkmbb.com/fitness/vertical-jump-power.md · JSON definition: https://tttkmbb.com/fitness/vertical-jump-power.json

## Purpose

Estimates lower-body power from a vertical jump height and body mass with the Sayers peak-power equation (60.7·height + 45.3·mass − 2055), the Harman peak-power equation and the Lewis average-power formula, plus take-off velocity and flight time.

**Use when:** You have a measured vertical jump (jump-and-reach or countermovement jump height) and body mass and want an estimate of peak or average muscular power in watts.

**Do not use when:** Force-plate power data are available (they measure power directly), or you need strength rather than power (use one-rep-max).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `jump_height_cm` | number | cm | required | Vertical jump height: jump-and-reach difference or countermovement-jump rise of the centre of mass. (min 10, max 150) |
| `body_mass_kg` | number | kg | required | Body mass in kilograms (the equations were fitted to adults). (min 30, max 300) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `sayers_peak_power_w` | number | W | 60.7 × jump_height_cm + 45.3 × body_mass_kg − 2055 (recommended equation). |
| `harman_peak_power_w` | number | W | 61.9 × jump_height_cm + 36.0 × body_mass_kg − 1822. |
| `lewis_average_power_w` | number | W | √4.9 × body_mass_kg × √(jump_height_m) × 9.81; underestimates true power and is kept for comparison with older norms. |
| `relative_peak_power_w_per_kg` | number | W/kg | Sayers peak power divided by body mass. |
| `takeoff_velocity_m_per_s` | number | m/s | √(2 × g × height) with g = 9.80665 m/s². |
| `flight_time_s` | number | s | 2 × takeoff_velocity / g (symmetric flight). |

## Formula

`Sayers: P_peak = 60.7·h_cm + 45.3·m_kg − 2055; Harman: P_peak = 61.9·h_cm + 36.0·m_kg − 1822; Lewis: P_avg = √4.9 × m_kg × √(h_cm/100) × 9.81; v_takeoff = √(2·g·h); t_flight = 2·v_takeoff / g`

Sayers et al. (1999) derived the equation on 108 college athletes and non-athletes from squat-jump heights against force-plate peak power (SEE ≈ 355 W) and found separate equations for men and women unnecessary; applied to countermovement-jump heights it over-estimates by about 2.7 %. Harman (1991) and Lewis are older estimates included for comparison.

## Data Sources

- Sayers SP, Harackiewicz DV, Harman EA, Frykman PN, Rosenstein MT (1999) Cross-validation of three jump power equations, Med Sci Sports Exerc 31:572-577 — https://pubmed.ncbi.nlm.nih.gov/10211854/ (peer_reviewed, retrieved 2026-09-24)
- Topend Sports – Vertical jump power calculators (Lewis, Harman, Sayers formulas) — https://www.topendsports.com/testing/vertical-jump-power.htm (reference, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/vertical-jump-power?jump_height_cm=…&body_mass_kg=…`
- `POST https://tttkmbb.com/api/v1/calculate/vertical-jump-power` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/vertical-jump-power · OpenAPI operationId `estimate_vertical_jump_power` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "vertical-jump-power", "inputs": {…}}`

## Example

- 50 cm jump, 75 kg: inputs `{"jump_height_cm":50,"body_mass_kg":75}` → `{"sayers_peak_power_w":4378,"harman_peak_power_w":3973,"lewis_average_power_w":1152,"relative_peak_power_w_per_kg":58.37,"takeoff_velocity_m_per_s":3.13,"flight_time_s":0.639}`
- 30 cm jump, 60 kg: inputs `{"jump_height_cm":30,"body_mass_kg":60}` → `{"sayers_peak_power_w":2484,"harman_peak_power_w":2195,"lewis_average_power_w":714,"relative_peak_power_w_per_kg":41.4,"takeoff_velocity_m_per_s":2.43,"flight_time_s":0.495}`

```
GET https://tttkmbb.com/api/v1/calculate/vertical-jump-power?jump_height_cm=50&body_mass_kg=75
```

## Limitations

Force-plate power data are available (they measure power directly), or you need strength rather than power (use one-rep-max). Sayers et al. (1999) derived the equation on 108 college athletes and non-athletes from squat-jump heights against force-plate peak power (SEE ≈ 355 W) and found separate equations for men and women unnecessary; applied to countermovement-jump heights it over-estimates by about 2.7 %. Harman (1991) and Lewis are older estimates included for comparison. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Why is the Lewis value so much lower?**

The Lewis nomogram estimates average power during the push-off and ignores body-mass displacement before take-off; Sayers found it under-estimates force-plate peak power by roughly 70 %. Use Sayers for peak power.

**Which jump height should I enter?**

Jump-and-reach (standing reach subtracted) or a countermovement jump measured by a mat or app. Heights from arm-swing jumps are higher and inflate the estimate.

## Related

- [One-Rep Max Calculator](https://tttkmbb.com/fitness/one-rep-max.md) — Maximal strength estimate for the same athlete.
- [Free Fall Calculator](https://tttkmbb.com/physics/free-fall.md) — Flight time and velocity for any drop or rise height.
- [Kinetic Energy Calculator](https://tttkmbb.com/physics/kinetic-energy.md) — Energy at take-off from mass and velocity.