The mechanism
Muscle pulls. The tendon keeps the spring shape.
When your foot presses into the ground, the calf muscles produce force and the Achilles tendon passes that force to the heel. The tissue lengthens by a few millimetres and stores strain energy. At toe-off, it shortens and returns that energy quickly.
The physics is simple: the area under the force–length curve is stored energy. In compact form, E = ∫ F dl. Tendon shape and loading determine whether the spring is compliant or stiff.
What researchers measured
Running adds energy, and the method changes the number.
Kharazi and colleagues followed the tendon in 11 adults who walked and ran on a treadmill. They measured the curved path with ultrasound and markers, then calculated force and energy from the force–length relationship.
| Movement | Speed | Energy |
|---|---|---|
| walking | 1.4 m/s | 7.8 J |
| slow running | 2.5 m/s | 9.5 J |
| fast running | 3.5 m/s | 11.3 J |
The same literature also contains a 35 J per step estimate for running at 4.5 m/s. Dividing it by 11.3 J gives 3.1. That comparison joins estimates from different protocols and assumptions. It shows how much the force measurement matters.
A tool for you
How much energy sits in a ten-centimetre difference?
Measure a jump from a squat and then a jump with a dip before take-off. Enter both heights and your body mass. The calculation shows the gravitational mechanical work associated with the height difference.
At 70 kg, an extra ten centimetres means 68.7 J of gravitational energy.
6.1 recoils of 11.3 J, as a scale reference
What the tool calculates
W = m × g × Δh, with g = 9.81 m/s². The height difference is converted from centimetres to metres, and the result is shown in joules. A real jump includes muscles, tendons, joints, and coordination. The calculator does not separate those contributions.
Limits
A biological spring has many settings.
The 11-person study used a treadmill and a force–length relationship obtained from isometric contractions. The 35 J estimate uses a different combination of force and geometry. These values give an order of magnitude for controlled movements, not a constant for every person.
Your jump includes the energy of the whole lower-limb system. Technique, surface, footwear, and measurement can all change the result. Stop if pain appears and keep the experiment in the realm of curiosity, not medical assessment.
Sources and scientific method
Where the numbers come from
- Kharazi et al., Scientific Reports, 2021In-vivo measurement of Achilles tendon loading and recoil in walking and running.
- Fletcher & Mullins, Physiological Reports, 2015Tendon energy estimates and the muscle cost that accompanies them.
- Fukashiro et al., Medicine & Science in Sports & Exercise, 1995Achilles tendon force and muscle work in three jumping tasks.
- Lai et al., Journal of the Royal Society Interface, 2016Running speed and modelled elastic energy in the plantar-flexor complex.
- Stearne et al., Journal of Biomechanics, 2016Elastic energy in the plantar aponeurosis during toe-off.
Values in the table are reported by the cited studies. Tool outputs use the declared mass, height, and gravitational acceleration.