# Human Biomechanics Calculator - Jump Height, Walking Speed, Cycling Power, Muscle Levers

> Physics of the body: jump height to takeoff speed, force and power; Froude number and walk–run speed; cycling power and climb time; MET calories; biceps force.

- URL: https://qilingtools.com/en/physics/biomechanics
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics), [Education](https://qilingtools.com/en/tags/education)
- Last updated: 2026-10-29
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Apply school physics to your own body: turn jump height or hang time into takeoff speed, ground force and power, and see why the Froude number makes you break into a run above a certain walking speed. Estimate energy with the ACSM equations and MET values, and compute cycling power from speed, gradient, wind, riding position and tyres, or the speed and climb time for a given power. The levers tab shows how hard the biceps pulls as a class-3 lever and how squat posture shifts load between knee and hip; all results are approximate and not medical or training advice.

## How to use

1. Choose a tab: jumping, walking & running, cycling power or levers in the body
2. Enter body mass and height, then set the jump height, speed, gradient, elbow angle or squat depth with the sliders
3. Read the result cards, animations and charts; some diagrams can be dragged directly (drag the hand to change the elbow angle)
4. Switch presets (gravity of other worlds, riding positions, road surfaces, famous climbs, activities) to compare cases

## Features

- Jumping: height, takeoff speed and hang time in any direction; push-off force and power; Sayers equation; animation with force curve
- Walking: Froude number, walk–run transition, step length and cadence, inverted-pendulum animation, Moon and Mars gravity
- Energy: ACSM walking and running equations, and MET calories for 30+ common activities
- Cycling: rolling, gravity and aero breakdown, power ↔ speed, famous climb times and VAM
- Levers: biceps force and elbow joint reaction with a draggable arm; squat knee and hip moments with a balance check

## FAQ

### How do you get push-off force from jump height?

Takeoff speed is v = √(2gh), about 2.97 m/s for a 45 cm jump. If the push-off distance (crouch depth) is d and the acceleration is constant, a = v²/(2d) and the average ground force is F = m(g + a) = mg(1 + h/d). A 70 kg person crouching 35 cm to jump 45 cm pushes with about 2.3 times body weight on average. Real force varies over time and peaks higher.

### Why do we switch to running when walking gets too fast?

In walking, the stance leg acts like an inverted pendulum, and the center of mass moves on an arc over it. That needs a centripetal acceleration v²/L, which only gravity can supply, so v²/L ≤ g, i.e. the Froude number Fr = v²/(gL) ≤ 1. With a 0.93 m leg the limit is about 3 m/s (11 km/h). In practice people switch to running at Fr ≈ 0.5, around 2.1 m/s. On the Moon, with 1/6 of Earth's gravity, the limit drops to about 1.2 m/s, which is why astronauts hopped.

### How many calories does running a kilometer burn?

The ACSM running equation gives a net oxygen cost of about 0.2 mL/kg/m. At roughly 5 kcal per liter of oxygen, that is about 1 kcal per kg per km, nearly independent of speed. A 70 kg runner burns about 350 kcal net over 5 km, a bit more including resting metabolism. Walking costs about half as much per km. Individual differences and terrain add error, so treat the numbers as estimates.

### Where does a cyclist's power go?

On the flat, air drag grows with speed squared and the power to beat it with speed cubed, so above 30 km/h it usually takes more than 80% of the total; rolling resistance is a small share. On climbs, gravity dominates and power-to-weight (W/kg) sets the speed. Lowering CdA with a tucked position helps most on the flat, and losing weight helps most uphill.

### Why does the biceps need hundreds of newtons to hold 5 kg?

The forearm is a class-3 lever: the elbow is the pivot, the biceps attaches only about 4 cm from it, and the hand is about 35 cm away. Torque balance means the muscle must pull about 35/4 ≈ 9 times the load, so about 490 N for 5 kg. In exchange, the hand moves about 9 times faster and farther than the muscle contracts.

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