Terminal Velocity

The speed that falling things settle into

Drop a stone off a high cliff and it speeds up as it falls — that much feels obvious. But it does not keep speeding up forever. Every object falling through air eventually reaches a steady, maximum speed and then falls at that speed the rest of the way down. This special speed is called the terminal velocity, and understanding it ties together gravity, drag, and Newton's laws into one elegant story.

A skydiver who jumps from a plane reaches a terminal velocity of around 55 metres per second (roughly 200 km/h) before their parachute opens. A raindrop reaches its own, much lower terminal velocity — which is lucky, because if raindrops kept accelerating all the way down from the clouds, they would hit the ground like bullets. This lesson explains exactly why falling things stop accelerating.

The tug-of-war between weight and drag

Two main forces act on anything falling through air:

• Weight (W) — the downward pull of gravity on the object's mass, given by W = m × g, where g ≈ 9.8 N/kg near Earth's surface. Weight is essentially constant throughout the fall. To revisit why this differs from mass, see weight vs mass.
• Drag (the air resistance force) — the upward push of the air against the falling object. Crucially, drag is not constant: it grows as the object speeds up. The faster you move, the more air particles you slam into each second, so the harder the air pushes back. To explore this push on its own, see air resistance and drag.

Whether the object speeds up, slows down, or holds steady depends on the resultant (net) force — the difference between weight and drag. This is the heart of balanced and unbalanced forces.

The four stages of a fall

Follow a skydiver from the moment they leave the plane and the whole story unfolds in stages.

Stage 1 — The instant of release. At the very start, the diver's speed is zero, so the drag force is zero. The only force acting is weight. The resultant force is at its maximum (just the weight), so by Newton's second law the diver accelerates at the full free-fall rate of about 9.8 m/s². They are speeding up as fast as they ever will.

Stage 2 — Speeding up, but less and less. As the diver gets faster, drag grows. Now the upward drag partly cancels the downward weight, so the resultant force shrinks. A smaller resultant force means a smaller acceleration. The diver is still getting faster — but the rate at which they speed up is dropping.

Stage 3 — Terminal velocity. Eventually the diver is moving fast enough that the upward drag force has grown to exactly equal the downward weight. Now the resultant force is zero. With no net force, there is no acceleration — and the diver falls at a constant speed. This steady speed is the terminal velocity.

Stage 4 — The parachute opens. When the parachute opens, the diver's surface area shoots up, so drag suddenly becomes much larger than weight. The resultant force now points upward, so the diver decelerates — they slow down. As they slow, drag falls again, until once more drag equals weight at a new, much lower terminal velocity, safe for landing.

Reading the velocity–time graph

The fall is beautifully captured on a velocity–time graph:

• It starts as a steep straight line — high, constant acceleration (gradient ≈ 9.8 m/s²) at the moment of release.
• The line then curves and flattens as acceleration falls (drag growing).
• It becomes horizontal when terminal velocity is reached — constant speed, zero acceleration.
• When the parachute opens the curve dips down (deceleration), then flattens into a new, lower horizontal line — the second, slower terminal velocity.

Remember: the gradient of a velocity–time graph is the acceleration. A horizontal line means zero gradient, hence zero acceleration — exactly the condition for terminal velocity.

Why mass and area change terminal velocity

The condition for terminal velocity is simply:

drag = weight

Anything that changes either side changes the terminal velocity.

• More mass → higher weight → higher terminal velocity. A heavier object needs more drag to balance its larger weight, and since drag grows with speed, the balance point happens at a faster speed. This is why a heavy ball-bearing falls faster than a light bead of the same shape.
• Larger surface area → more drag at any given speed → lower terminal velocity. A wide, flat or fluffy object generates lots of drag even when moving slowly, so drag equals weight at a lower speed. This is the whole point of a parachute.
• More streamlined shape → less drag → higher terminal velocity. A skydiver who tucks into a head-first dive reduces their area and can exceed 90 m/s.

This explains the classic feather-and-coin puzzle. In air, the feather has a tiny weight but a large area, so it reaches a very low terminal velocity almost immediately and drifts down slowly. The coin has more weight and a small area, so it accelerates to a higher speed. But in a vacuum, with no air, there is no drag and therefore no terminal velocity — both objects accelerate together at g and land at exactly the same moment. Astronaut David Scott famously demonstrated this on the airless Moon in 1971 by dropping a hammer and a feather together.

A worked example

Worked example. A skydiver of mass 75 kg falls at terminal velocity. Take g = 9.8 N/kg.

What is the size of the drag force acting on them?

At terminal velocity the forces balance, so drag = weight:

W = m × g = 75 kg × 9.8 N/kg = 735 N

So the upward drag force is also 735 N, exactly cancelling the weight. The resultant force is zero, which is why the diver falls at a steady speed.

What is their acceleration at this moment?

By Newton's second law, a = F ÷ m, and the resultant force F is zero, so:

a = 0 ÷ 75 = 0 m/s²

Zero acceleration confirms constant velocity. (Contrast this with the very first instant of the fall, when drag was zero, the resultant force was the full 735 N weight, and a = 735 ÷ 75 = 9.8 m/s².) These ideas come straight from Newton's laws of motion.

Why terminal velocity matters

Terminal velocity is not just a curiosity for skydivers. It sets the speed at which raindrops, hailstones, dust, seeds, and pollen fall to the ground, shaping weather and ecology. Engineers use it to design parachutes, drag chutes on dragsters and landing aircraft, and the safe descent of spacecraft and supply drops. It is also a perfect real-world demonstration that forces, not speeds, cause acceleration — the deepest lesson in Newtonian mechanics.

Try it yourself! 🧪

Measure terminal velocity with coffee filters — completely safe.

Stacked paper coffee filters are ideal: they are light, have a fixed shape, and reach terminal velocity within a fraction of a second, so they fall at a steady, measurable speed for most of the drop.

1. Stand on a chair or step (with someone steadying you) and hold one coffee filter at a fixed, marked height — say 2.0 m.
2. Drop it and use a stopwatch (or a phone's slow-motion video) to time how long it takes to reach the floor. Because it reaches terminal velocity almost instantly, its average speed over the drop is very close to its terminal velocity. Estimate it as speed = distance ÷ time.
3. Now nest two filters together and drop them from the same height. Two filters have double the weight but almost the same surface area — so theory predicts a higher terminal velocity (a shorter fall time).
4. Try four filters, then eight. Plot fall time (or speed) against the number of filters.

You should find that adding mass while keeping the area the same makes them fall faster — exactly as drag = weight predicts. By keeping the shape constant and changing only the weight, you have isolated a single variable, just as a real physicist would.