Nobody's pushing you, so
why does pumping your legs make a swing go higher?
You're not kicking off the ground, yet the swing climbs higher every time you pump it. The energy comes from you — from raising and lowering your body. Stand up at the very bottom, crouch at the ends. That sequence quietly pours energy into the swing, bit by bit.
A child is on a swing at the park. At first, someone was pushing their back.
Then they say "I'm okay now" and start pumping on their own. Their feet never touch the ground — they're just bending and straightening their knees in mid-air.
And yet the swing keeps climbing higher. If someone asked you "there's no one pushing — so where's the force coming from?", could you answer?
There are only two reasons
As you pass through the lowest point of the swing, your bottom presses hard against the seat. Standing up there takes more force than usual. That "extra effort" turns into energy for the swing.
At the ends of the swing, it pauses for an instant and your body feels weightless. Crouching there gives back only a little energy. Raise yourself when heavy, lower yourself when light — that difference adds up.
In short, pumping a swing is repeatedly "lifting a heavy load, then setting it down once it's light." Since the lifting work is bigger than the lowering work, the difference between the two makes the swing grow.
Standing pump: the centre of gravity "cuts inside, then swings back out"
The centre of an object's weight is called its centre of gravity. Standing brings it closer to the pivot at the top; crouching moves it farther away. Figure 1 traces the path of the centre of gravity for someone pumping while standing.
At the very bottom, the swing is curving through an arc. Anything moving along a curve feels pushed outward. So at the bottom, your weight gets extra "push" added on top.
Standing up here does something else useful too. Just as a figure skater spins faster by pulling their arms in, a body that moves closer to the pivot speeds up. That extra speed carries you higher at the next end.
Sitting pump: a different mechanism drives the swing
Pumping while seated works a bit differently. You lean back at the rear end and stretch your legs forward. At the front end, you sit up and pull your legs in.
As you lean back, your hands pull on the chains. The reaction pushes the seat forward. It's a bit like using your own body to push your own back.
Figure 2 compares the timing of the two pumping styles. On the left, standing pumping stands up twice per full swing cycle. On the right, sitting pumping leans back once and sits up once per cycle.
Standing and crouching on a motionless swing barely produces any motion at all. That's because the "heavy at the bottom, light at the ends" difference only exists once the swing is already moving. That's why, before standing-pumping, people sit and pump first, or kick off the ground to get a little motion going.
Try standing at the ends on purpose and crouching at the bottom instead. Now you're "raising when light, lowering when heavy," and the swing gradually loses height. The same motions can either add or subtract energy — timing alone decides which.
Summary
Pumping a swing works because you lift your body at the very bottom of the swing and lower it at the ends. Since your body is heavy at the bottom and light at the ends, the lifting work is bigger than the lowering work. That difference builds up as swing energy with every cycle. Sitting pumping uses a different method: pushing the seat forward through the reaction of leaning your body back.
Even with no one to push you,
raise yourself when heavy and lower yourself when light, and the swing will grow.
How to match your timing when someone else is pushing your back is explained in Why don't bridges and buildings collapse when they sway in the wind?. Changing your body's shape to control motion is also the theme of Why can cats always land on their feet?.
- Get the swing moving a little first, then keep standing at the bottom and crouching at the ends for about 10 cycles. Watch the swing grow bigger.
- Next, try standing at the ends on purpose and crouching at the bottom. The swing should shrink.
- You can try this at home too. Tie a coin to a piece of thread to make a pendulum, and pinch the top end between your fingers. Pull the thread up slightly each time the pendulum passes the bottom, and loosen it slightly at the ends — the swing will grow.
On a real swing, always keep a firm grip on the chains throughout, and make sure no one else is nearby.
Want to go deeper? — terms, formulas, and links to the curriculumWe label each part by level, from middle-school science up to university-level courses
- MSCovered in middle-school science
- HSCovered in high-school "Basic Physics" / "Physics"
- HS+High-school advanced content, or textbook sidebar material
- UnivNot taught in high school — university-level mechanics/vibration theory
- ResearchNot yet settled even at university level — an open question researchers are still studying
MSTerminology: this phenomenon has a name
- Centre of gravity: the point where an object's weight can be treated as concentrated. It rises when you stand and falls when you crouch.
- Isochronism of the pendulum: for small swings, the time for one full cycle stays roughly the same regardless of how wide the swing is.
- Parametric excitation: rather than pushing from outside, this grows a swing by periodically changing a quantity that governs the motion — such as a pendulum's length. Standing-pumping is the classic example.
MSHSWorking it out: how much higher do you go by standing at the bottom?
Suppose the distance from the pivot to the centre of gravity is 2.0 metres when crouching and 1.8 metres when standing. Assume you stand up sharply at the instant you pass through the bottom at 3 metres per second. At the moment you stand, the rotational momentum around the pivot (angular momentum) is conserved, so your speed is said to increase in inverse proportion to the length.
| Pivot-to-centre-of-gravity length while crouching, r1 | 2.0 metres |
| Pivot-to-centre-of-gravity length while standing, r2 | 1.8 metres |
| Speed at the bottom, v | 3 metres per second |
| Twice the gravitational acceleration, g | 19.6 metres per second squared |
| Height reachable while staying crouched (speed squared) | 3 × 3 = 9 |
| That height (metres) | 9 ÷ 19.6 ≒ 0.46 |
| Ratio of lengths when standing | 2.0 ÷ 1.8 ≒ 1.11 |
| Speed right after standing (metres per second) | 3 × 1.11 ≒ 3.33 |
| Speed squared | 3.33 × 3.33 ≒ 11.1 |
| Height reachable after standing (metres) | 11.1 ÷ 19.6 ≒ 0.57 |
| Factor by which the height increased | 0.57 ÷ 0.46 ≒ 1.24 |
Raising the centre of gravity by just 20 centimetres increases the height reached by about 1.24 times. This happens twice per cycle, so over a few cycles the swing visibly grows. This is an idealised calculation assuming you can stand up instantly, though. In reality, standing up takes time, and air resistance and chain friction leak away energy, so the actual gain is smaller than this. Units: length in metres, speed in metres per second.
HSHS+Seeing "raise when heavy, lower when light" in terms of force
HSAt the very bottom, the swing is moving in a circular arc. Since a force toward the centre of the circle is needed, the chain's pulling force is greater than your body weight. You learn that "mass × speed squared ÷ radius" is added on top of your weight. At the ends, meanwhile, the speed is zero, so the chain's pulling force is less than your body weight. Since the work done moving the centre of gravity is "force × distance," even over the same 20 centimetres, the work done lifting at the bottom is greater than the work returned by lowering at the ends.
HS+Assuming the swing angle is small, consider the swing angle right after standing up. The square of the angle is said to scale as the cube of the length ratio. In the example above, the length ratio is about 1.11, so the angle squared works out to about 1.4 times. Since the angle doesn't change when crouching at the ends, this growth compounds every half-cycle. Because the growth is "proportional to the current swing width," nothing grows if the swing width is zero. This is why, as noted in the callout, a still swing can't be started moving by standing-pumping alone.
UnivStanding pump is close to "parametric resonance," sitting pump is close to "forced vibration"
Motion that periodically changes a pendulum's length is described by an equation of the Mathieu-equation type. It's known that when the length is varied at twice the swing's own frequency, there's a region where the swing width grows exponentially. This is parametric resonance, corresponding to "standing twice per cycle" in Figure 2. Unlike ordinary resonance from an external push, it cannot grow starting from zero swing. Sitting-pumping, by contrast, rotates the upper body and legs to apply a periodic force to the seat and chains. This is closer to forced vibration, pushing at the same frequency as the swing, and is said to be able to build motion even from a standstill. Some analyses suggest that real sitting-pumping mixes both mechanisms.
ResearchWhat's still not fully understood
- What timing do people actually use when pumping? Measurements on adults have reported that pumping timing gradually shifts as the swing grows larger. Whether that shifted timing is actually the most efficient one is still debated.
- The optimal pumping style at large swing widths. As the swing width grows, the pendulum's isochronism breaks down, and simple formulas no longer apply. Which pumping style gets you highest fastest is said to depend on the conditions.
- How do children learn to pump without being taught? Swings are used in research as a case study in motor learning — matching one's own body movements to the swing's motion. Which sensory cues are being used is not yet clear.
In other words, even this article only describes "what's understood so far." Even a single piece of playground equipment still holds unanswered questions.
Links to the curriculum (by level)
| Level | Subject / Unit | Where in this article |
|---|---|---|
| MS | Science — mechanical energy, pendulums | Trading height for speed, centre of gravity |
| HS | Basic Physics — work and energy / Physics — circular motion | Why the body feels heavier at the bottom, calculating the height gained |
| HS+ | Physics — angular momentum (advanced) | Why standing speeds you up, how the angle grows |
| Univ | Mechanics — vibration theory | The difference between parametric resonance and forced vibration |
| Research | Motor learning, nonlinear vibration | Timing of human pumping, optimisation at large amplitude |
| — | Everyday connections | Playground swings, pendulum experiments |
- Case, W. B., & Swanson, M. A. (1990). The pumping of a swing from the seated position. American Journal of Physics, 58(5), 463–467.
- Wirkus, S., Rand, R., & Ruina, A. (1998). How to pump a swing. The College Mathematics Journal, 29(4), 266–275.
- Post, A. A., de Groot, G., Daffertshofer, A., & Beek, P. J. (2007). Pumping a playground swing. Motor Control, 11(2), 136–150.
- High-school "Basic Physics" / "Physics" textbooks (units on work and energy, circular motion, simple pendulums)
※This article is a general-audience science explainer. The figures given are approximate, meant to aid understanding of the underlying mechanism. When using playground equipment, follow the posted signage and any instructions from the facility's staff.