A see-saw is a first-class lever — a rigid beam pivoting on a central fulcrum, with a load applied at each end. It solves the problem of trading force for distance across a fixed pivot: a heavier load on a shorter arm balances a lighter load on a longer arm. The beam rotates until the moments on each side equalise, then either holds static or oscillates. You see this principle everywhere from playground teeter-totters to weighbridges and counterweighted theatre rigging.
See-saw Interactive Calculator
Vary rider masses and lever-arm distances to see the torque balance, required seat position, and beam response.
Equation Used
The calculator applies the see-saw balance equation m1 * L1 = m2 * L2. The worked example uses kg times metres as the moment comparison, so the same mass moment units are shown here. Multiplying both sides by 9.81 would convert the moments to N*m without changing the balance condition.
- Mass is used as kg force equivalent, matching the worked example.
- Beam weight and seat weight are neglected.
- Loads act vertically at the selected arm distances from the fulcrum.
How the See-saw Actually Works
A see-saw works on torque balance about the fulcrum. Each side of the beam generates a moment equal to the applied force multiplied by its perpendicular distance from the pivot — so a 30 kg child sitting 1.5 m from the fulcrum produces 441 N·m of torque, and balancing requires the same torque on the opposite side. If the other rider is 60 kg, they need to sit at 0.75 m to match it. That distance ratio is the mechanical advantage of the lever, and it's why a small child can lift a much larger adult by sliding outward along the beam.
The geometry is deliberately simple because the failure modes are mostly mechanical, not kinematic. The pivot bushing or bearing must carry the full sum of both end loads — in the 30 kg + 60 kg case, that's 90 kg of vertical reaction plus dynamic loads from bouncing, which can spike to 2-3× static. If the pivot has play above roughly 1 mm radial clearance, the beam wobbles laterally and the riders feel the slop. If the beam itself flexes, you lose travel at the ends and the ride feels mushy. A typical playground see-saw uses a 60 mm steel tube beam to keep deflection under L/360 at full load.
Get the centre of gravity wrong and the see-saw won't return to neutral. The beam, the seats, and any handles must balance about the fulcrum when unloaded — otherwise the heavy end always sits down, and riders have to fight that bias every cycle. Manufacturers like Miracle Recreation and Landscape Structures machine the pivot location to within ±2 mm of the beam's true centre of mass for exactly this reason.
Key Components
- Beam (lever arm): The rigid bar that transmits force from one end to the other through the fulcrum. Stiffness matters — a 2.4 m playground beam typically uses a 60 mm OD × 3 mm wall steel tube to keep mid-span deflection under 7 mm at 100 kg per end.
- Fulcrum (pivot): The pivot point about which the beam rotates. Carries the full vertical sum of both end loads plus dynamic shock. Most production see-saws use a sealed bushing or a pair of flanged bronze bearings rated for at least 5 kN combined radial load.
- Seats or load points: Define the effective lever arm length on each side. Seat centre-to-fulcrum distance sets the mechanical advantage — a 1.2 m arm on each side gives a 1:1 ratio, suitable for two riders of similar mass.
- End stops or bumpers: Limit beam rotation to typically ±15-25° and absorb impact when one end strikes the ground. Rubber bumpers prevent the spinal jolt that sent so many 1970s steel-on-concrete see-saws into early retirement.
- Handles or grab points: Give riders something to pull against during the down-stroke. Without them, a rider can't actively drive the oscillation — you just sit and wait for the other person to push.
Where the See-saw Is Used
The see-saw geometry shows up far beyond the playground. Anywhere a single pivot trades force for distance across a beam, you're looking at the same mechanism — and the engineering decisions are identical: pivot load capacity, beam stiffness, and arm-length ratio for the desired mechanical advantage. The principle scales from gram-scale laboratory balances to multi-tonne industrial counterweights.
- Playground equipment: Miracle Recreation's classic 2-seat teeter-totter uses a 2.4 m steel beam on a sealed pivot, rated for 2 × 90 kg riders.
- Laboratory instruments: Mettler Toledo equal-arm analytical balances use a knife-edge fulcrum with arms machined to ±0.005 mm length matching for sub-milligram accuracy.
- Theatre and stage rigging: Counterweighted fly systems use see-saw geometry where stage scenery on one arm balances against lead bricks on the other, allowing one operator to fly hundreds of kg of set.
- Weighbridges: Mechanical truck scales like the legacy Fairbanks-Morse beam scales used compound lever arrangements where the primary beam is a see-saw scaled to read off a sliding poise.
- Industrial pump jacks: Oilfield pumpjacks (the 'nodding donkey' rigs from Lufkin and similar) use a walking beam pivoted on a Sampson post — a see-saw driving a downhole rod pump with a counterweight on the back arm.
- Children's ride-on toys: Little Tikes and Step2 rocking see-saws scale the geometry to 800 mm beams for toddlers, with travel limited to ±10° by moulded bumpers.
The Formula Behind the See-saw
The balance equation tells you where to place loads on the beam, or what load you need at a known distance to lift a given weight. The interesting range isn't the perfectly balanced static case — it's what happens when one rider is much heavier or lighter than the other, and how far they have to slide along the beam to make the see-saw work. At a 1:1 mass ratio you sit at equal distances and the geometry is trivial. At a 2:1 mass ratio the heavier rider must sit at half the distance, which on a 1.2 m arm puts them only 600 mm from the pivot — close enough that they barely move vertically during the cycle. Push the ratio past 3:1 and the heavier rider is so close to the fulcrum that the see-saw effectively becomes a one-sided ride.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| F1 | Force (weight) applied at end 1 | N | lbf |
| L1 | Distance from fulcrum to end 1 load point | m | ft |
| F2 | Force (weight) applied at end 2 | N | lbf |
| L2 | Distance from fulcrum to end 2 load point | m | ft |
Worked Example: See-saw in a school playground teeter-totter
A primary school in Christchurch is fitting a 2.4 m steel-tube see-saw beam between two pupils of unequal mass. The lighter pupil weighs 25 kg, the heavier pupil weighs 45 kg. The lighter pupil sits at the standard end position, 1.2 m from the central fulcrum. The teacher needs to know where the heavier pupil should sit to balance the beam, and what happens at the edges of the typical mass-ratio range a school sees across age groups.
Given
- F1 = 25 × 9.81 = 245 N
- L1 = 1.2 m
- F2 = 45 × 9.81 = 441 N
- L2 = ? m
Solution
Step 1 — apply the moment-balance equation and solve for L2 at the nominal mass pairing of 25 kg and 45 kg:
So the heavier pupil sits 667 mm from the fulcrum — about 533 mm closer in than the lighter pupil. That's a comfortable, usable position on a standard 1.2 m half-beam, with plenty of room for the seat and handles.
Step 2 — at the low end of the typical school mass-ratio range, two pupils of nearly equal mass (say 30 kg and 32 kg):
Both pupils sit almost at the standard end positions, only 76 mm difference. The see-saw feels symmetric, both riders get full vertical travel of roughly ±300 mm at the seat, and the cycle is easy to drive.
Step 3 — at the high end of the range, an older pupil paired with a much younger one (20 kg and 60 kg, a 3:1 ratio):
The heavier rider is now only 400 mm from the fulcrum. Their vertical travel collapses to roughly ±100 mm — barely enough motion to feel like a ride. Below this point the see-saw stops working as a shared activity and becomes a one-sided lift, where the lighter rider does all the work and the heavier rider essentially sits still.
Result
The heavier 45 kg pupil should sit 667 mm from the fulcrum to balance the lighter 25 kg pupil at the standard 1. 2 m position. That puts the two riders in usable, intuitive positions with full travel on both ends. Across the typical school range, equal-mass pairings let both pupils sit near the ends and enjoy full ±300 mm vertical travel, while a 3:1 mismatch crushes the heavier rider's travel to ±100 mm and the see-saw stops feeling like a shared ride. If you measure a beam that won't balance at the calculated position, the most likely causes are: (1) the beam's own centre of gravity offset from the fulcrum by more than ±5 mm, biasing one side down regardless of rider position; (2) seat hardware mass differences left over from a one-sided repair, adding 1-2 kg of unaccounted weight at one end; or (3) a pivot bushing that's binding on one side, requiring extra torque to break free and masking true balance.
See-saw vs Alternatives
The see-saw is a first-class lever, but it's not the only way to trade force for distance about a pivot. The choice between a see-saw, a wheelbarrow-style second-class lever, and a fishing-rod-style third-class lever comes down to where the load sits relative to the effort and the pivot — and that choice changes mechanical advantage, range of motion, and structural loading dramatically.
| Property | See-saw (1st class lever) | Wheelbarrow (2nd class lever) | Fishing rod (3rd class lever) |
|---|---|---|---|
| Mechanical advantage range | 0.1× to 10× (variable, depends on arm ratio) | Always > 1 (effort always > load distance from pivot) | Always < 1 (effort always < load distance from pivot) |
| Pivot reaction force | Sum of both end loads (highest) | Difference between effort and load (moderate) | Difference between effort and load (moderate) |
| Range of motion at output | Equal to input × arm ratio (bidirectional, ±20° typical) | Smaller than input motion | Larger than input motion (motion amplifier) |
| Typical application fit | Balance, oscillation, weighing | Heavy lifting with reduced effort | Speed and reach amplification |
| Beam stiffness requirement | High — load on both sides of pivot causes bending | Lower — load between pivot and effort | Lower — single-sided cantilever |
| Cost and complexity | Low — single pivot, symmetric beam | Low — single pivot, asymmetric loading | Low — single pivot, end effort |
Frequently Asked Questions About See-saw
The beam's centre of gravity is offset from the fulcrum. This happens when one seat is heavier than the other, when one side has been repaired with different hardware, or when the pivot was installed off-centre during fabrication. Lift the unloaded beam to horizontal and let go — if it always falls the same way, it's a CG offset, not a bearing problem.
The fix is to add counterweight to the light end until the unloaded beam holds horizontal. On a 2.4 m beam, every 100 g added at the end shifts the CG by roughly 1 mm. A bias of more than ±5 mm CG offset is enough to feel during a ride.
The pivot has to carry the sum of both end weights plus dynamic shock. Two 90 kg adults give 180 kg static, but bouncing — especially the slam when one end hits its bumper — spikes the load to 2-3× static. Size the bearing for at least 5.4 kN radial capacity to give margin.
A pair of flanged bronze bushings or a sealed deep-groove ball bearing in a 25-30 mm bore works for adult-rated see-saws. Avoid plain steel-on-steel pivots — they wear into an oval within a season of outdoor use and develop the lateral wobble riders complain about.
Mushy feel almost always traces to beam bending, not pivot slop. A 60 mm OD × 3 mm wall steel tube spanning 2.4 m deflects roughly 7 mm at mid-span under 100 kg per end — that doesn't sound like much, but the rider feels it as lost travel and a soft top-of-stroke.
If you want a crisp ride, step up to a 75 mm OD × 4 mm wall tube or add a top chord to make the beam a shallow truss. Either change cuts mid-span deflection roughly in half and makes the ride feel like the beam is actually transmitting force end-to-end.
Depends on whether you need bidirectional motion or just lifting. A see-saw (first-class lever) gives you motion in both directions about the pivot, so it works for tipping a part forward AND backward from a single handle. A wheelbarrow layout (second-class lever) gives more mechanical advantage at the cost of one-way motion only.
For a tipping fixture that needs to load and unload from the same side, the see-saw geometry wins. For a pure lifting fixture where you only ever raise one direction, a second-class lever uses a smaller pivot bearing because the reaction force is the difference between load and effort, not the sum.
Practically, around 2.5:1. Beyond that ratio the heavier rider has to sit so close to the fulcrum that their vertical travel drops below about 150 mm — the ride stops feeling like a ride and becomes a lifting exercise for the lighter rider. At 3:1 you're at 100 mm of travel for the heavier rider, which is the threshold where most kids give up and walk away.
If you genuinely need to handle wide mass ratios, design in adjustable seat positions with locking pins at 100-150 mm increments along the beam, the way some 1980s Game Time playground sets did.
The pivot shaft is bending under load and pinching the bearings. This shows up when the bearing housing is too narrow relative to the shaft length, or when the shaft diameter is undersized for the moment generated by off-axis loading from riders shifting sideways.
Check by removing the beam and pushing the shaft sideways at the bearing — any visible deflection means the shaft is undersized. A 25 mm shaft in a 60 mm-wide bearing housing handles two-adult loading; drop to 20 mm and you'll feel binding within months. Also check that the two bearings are coaxial within 0.1 mm — misalignment of more than that loads the inner races diagonally and causes the same binding symptom.
References & Further Reading
- Wikipedia contributors. Seesaw. Wikipedia
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