Fulcrum Calculator (where to put the pivot of a lever)

Understanding the fulcrum calculator — concept and principle

This calculator finds where to put the pivot (fulcrum) of a lever so that a load at one end balances an effort at the other, optionally including the lever's own weight. It also gives the lever ratio and the force the fulcrum must carry. It is useful for seesaws, pry bars, balance beams and physics problems.

The pivot sits 0.75 m from the 60 kg load, so each side has the same moment and the pivot carries both weights.

How it is calculated

Balance about the fulcrum: F_L × x = F_E × (L − x) + W × (L/2 − x)

x = L × (F_E + W/2) ÷ (F_L + F_E + W)

For a light bar: x = L × F_E ÷ (F_L + F_E)

Force on the fulcrum = F_L + F_E + W

x is measured from the load end, L is the lever length, W the lever's own mass acting at its middle.
Masses in kg stand for their weights; the fulcrum force is also shown in newtons (× 9.80665).

The principle

A rigid bar is balanced when the turning effects (torques) on each side of the pivot cancel. Torque is force times its distance from the pivot, so a small force far away can balance a large force close by. That is why the fulcrum sits closer to the heavier end and why the arm ratio equals the force ratio. The bar also must not move up or down, so the fulcrum pushes up with the sum of all the weights.

Worked example

Default inputs: lever 3 m, load 60 kg, effort 20 kg, lever mass 0.

x = 3 × 20 ÷ (60 + 20) = 0.75 m from the load end.
Effort arm = 3 − 0.75 = 2.25 m.
Lever ratio = 2.25 ÷ 0.75 = 3×, matching 60 ÷ 20.
Fulcrum force = 60 + 20 = 80 kg, or 80 × 9.80665 = 785 N.

Each point is the calculator re-run with only “Length of the lever (m)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Length of the lever (m)	Fulcrum distance from the load end (m)
0.75	0.188
1.5	0.375
2.25	0.563
3	0.75
3.75	0.938
4.5	1.125
6	1.5

How to read the result

The lever ratio is the mechanical advantage: an effort three times smaller balances the load, but the effort end moves three times further. Including a heavy bar shifts the fulcrum towards the middle. Check that the fulcrum and bar can carry the full fulcrum force.

Common mistakes

Measuring x from the wrong end.
Forgetting the bar's weight when it is heavy compared with the loads.
Expecting the lever to reduce the work needed. It trades force for distance.

Keep in mind: This is a static balance for an ideal rigid lever. For lifting heavy loads, check the strength of the bar and fulcrum and follow safe lifting practice.

Frequently asked questions

Where should the fulcrum go for equal weights?

Exactly in the middle.

What class of lever is this?

A first-class lever, with the fulcrum between the load and the effort.

Does the bar's weight matter?

Yes, when it is not small compared with the loads; it acts at the middle of the bar.

Sources: OpenStax, University Physics Volume 1 (2016), section 12.1 "Conditions for Static Equilibrium"

Checked 9 Nov 2026. OpenStax, University Physics Volume 1 (2016), §12.1 “Conditions for Static Equilibrium” (ΣF = 0 and Στ = 0; the weight of a uniform body acts at its centre of mass).

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