The biomechanics of a step
Walking is controlled falling.
As you step, your body rises and falls over the stance leg like an inverted pendulum. Some of the energy in one phase becomes the energy of the next.
Measurements by G. A. Cavagna, H. Thys, and A. Zamboni found about 65% mechanical recovery at intermediate walking speeds.
01 / the mechanism
One foot on the ground. Two forms of energy.
In a step, the body’s centre of mass traces an arc above the foot touching the ground. As the body rises, gravitational potential energy increases. As it falls, that energy returns as motion.
Picture a long ruler balanced at one point, with its weight at the top. As the ruler falls, its speed increases. Walking uses a controlled version of the same idea: the straight leg is the support point, and the body passes over it.
The exchange is not perfect. Muscles still lift and reposition the limbs, and the next step needs energy at ground contact. The pendulum nevertheless reduces the work muscles would do if they lifted and accelerated the body’s centre separately on every step.
02 / the reversal
Walking and running save energy differently.
In walking, potential and kinetic energy exchange like a pendulum. In running, the body relies more on elastic springs in tendons and muscles.
At the top of the running range, the difference from walking is 61 percentage points. Both values describe external mechanical recovery, not total metabolic efficiency.
That is why running is not walking turned up faster. In walking, the legs exchange energy as two arms of a pendulum. In running, each landing loads tendons and muscles like springs that release immediately.
Speed has a mechanical limit, but the body does not experience it as a switch. Cadence, fatigue, footwear, slope, and comfort change when running becomes preferable.
03 / the reference point
Speed only makes sense with leg length.
A speed of 2 metres per second means something different for two people with different leg lengths. The Froude number puts speed on the same mechanical scale.
Fr = v² / (g × ℓ). Here, v is speed in metres per second, g is gravitational acceleration, and ℓ is leg length.
In the literature on the walk-to-run transition, Fr = 0.5 is a common reference point. For a 0.90-metre leg, it corresponds to about 2.10 metres per second, or 7.56 kilometres per hour.
Fr = 0.5
The limit of the reference. Studies find the transition at speeds around 1.9–2.1 metres per second and at different Froude values. The formula compares mechanics, but it cannot decide on its own whether a person is walking or running.
04 / measure yourself
the pendulum instrument
Put your walk on the same scale.
Measure your leg from the floor to the hip crease. Then cover the chosen distance at a normal walking pace and stop the timer.
The timer is ready.
Your walk is below Fr = 0.5. The inverted pendulum is still the useful model at this speed.
At the same leg length, the theoretical speed associated with Fr = 0.5 is 2.10 m/s.
The calculation uses v = distance / time and Fr = v² / (g × ℓ), with g = 9.81 metres per second squared. It is an indicative mechanical model, not a medical or laboratory assessment.
05 / outside the formula
A good number knows where it stops.
The 65% figure refers to the body’s external mechanical work. It does not tell you how much oxygen you use, how hard each muscle works, or how much energy it takes to move the legs.
The Froude number helps compare people with different leg lengths. It is not a diagnosis and cannot predict your walk-to-run transition by itself. In experiments, real behaviour spreads around the reference.
sources and method
Where the figure and formula come from.
The 65% figure comes from measurements of external work in walking and running. The Froude-number formula normalizes speed to leg length. Values are rounded on the page, and the instrument recalculates whenever an input changes.
- G. A. Cavagna, H. Thys, and A. Zamboni, The sources of external work in level walking and running, Journal of Physiology, 1976.
- R. M. Alexander, Energy-saving mechanisms in walking and running, Journal of Experimental Biology, 1991.
- N. K. Bohnsack and colleagues, Cadence as an indicator of the walk-to-run transition, 2023.