Lever equilibrium calculator

Type exactly three of F₁ [N], r₁ [m], F₂ [N], r₂ [m]. The calculator computes the fourth and the shared moment: 20 N on 0.5 m against 0.2 m gives F₂ = 50 N and M = 10 N·m. Model at 90°.

Single torque: M = F·r·sinα (here α = 90°). Force: F = m·a.

Inputs

Result

Force F₁, Arm r₁, Force F₂ and Arm r₂. The result shows up here.

How it works

F₁ F₂ r₁ r₂ F₁r₁ = F₂r₂
Equilibrium: moments about the fulcrum cancel.

With perpendicular arms the balance is F₁ r₁ = F₂ r₂. The shared moment is M = F₁ r₁. At 20 N, r₁ = 0.5 m and r₂ = 0.2 m you get F₂ = 50 N, because 20 × 0.5 = 10 and 10 / 0.2 = 50. That same M = 10 N·m sits on both sides of the fulcrum.

Four fields: forces in newtons, arms in meters. Leave exactly one blank: that is the unknown. A typed 0 in a force is a real zero, not a gap to solve. A comma and a period in 0.5 are the same arm.

Two blanks or four filled values are rejected. Arms must be positive: r = 0 is the axis, not an arm. The model assumes 90°, so sinα = 1 and you do not type an angle.

An angled force is first M = F r sinα on the torque page, then you come back with the perpendicular part. F = m a is a general force, not a two-arm balance.

The inverse: F₂ = 50 N, r₂ = 0.2 m and r₁ = 0.5 m give F₁ = 20 N. Solving for an arm? At F₁ = 20 N, F₂ = 50 N and r₁ = 0.5 m you get r₂ = 0.2 m.

Type 20, 0.5 and 0.2, leave F₂ blank, click Calculate, and match 50 N plus M = 10 N·m. Then clear and leave a different field blank. A wrench or a seesaw is the same balance.

How to use

  1. Type exactly three of F₁, r₁, F₂, r₂. Leave one field blank: that is the unknown.
  2. For example F₁ = 20 N, r₁ = 0.5 m, r₂ = 0.2 m, and F₂ blank.
  3. Click Calculate. F₂ comes out 50 N, shared moment M = 10 N·m.
  4. Two blanks or four filled values are rejected. Typed 0 is zero, not a gap. Arms must be positive.
  5. For forces not at 90°, open torque as M = F r sinα, then return to the balance.

Formula

F1·r1 = F2·r2

M = F1·r1

F₁, r₁, F₂, and r₂ on the lever

A lever in balance: F₁ r₁ = F₂ r₂. 20 N on 0.5 m against r₂ = 0.2 m gives F₂ = 50 N and M = 10 N·m. Angle 90°.

F₁
Force on one side [N]. 20 N. Three givens, the calculator fills the fourth.
r₁
Arm of F₁ [m]. 0.5 m. A zero arm does not divide.
F₂
Force on the other side [N]. 50 N at r₂ = 0.2 m and M = 10 N·m.
r₂
Arm of F₂ [m]. 0.2 m. Shorter arm, larger F₂.

Real-life examples

Example 1

F₁ = 20, r₁ = 0.5, r₂ = 0.2 → F₂ = 50.

Example 2

F₂ = 50, r₁ = 0.5, r₂ = 0.2.

Example 3

F₁ = 10, r₁ = 1, F₂ = 40.

Example 4

F₁ = 25, F₂ = 50, r₂ = 0.4.

Example 5

F₁ = 400 N, r₁ = 1.2 m, r₂ = 0.8 m.

Example 6

F₁ = 100 N, r₁ = 0.8 m, F₂ = 800 N.

Example 7

F₁ = F₂ = 5 N, r₁ = 0.3 m → r₂.

Example 8

F₁ = 200 N, r₁ = 0.1 m, r₂ = 0.5 m.

Example 9

F₁ = 150 N, r₁ = 1.5 m, F₂ = 750 N.

Ways to use this calculator

  • You compute F₂ = 50 N from 20 N on 0.5 m against 0.2 m.
  • You solve for a missing arm when F₁, F₂ and the other r are known.

Related calculators

Force F = m·a
Two forces at the lever ends when the moments balance.
Torque
Torque from force F, lever arm length, and the angle.
Moment of inertia (point mass)
Point-mass moment of inertia: mass times r squared.

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Frequently asked questions

What F₂ balances F₁ = 20 N, r₁ = 0.5 m, r₂ = 0.2 m?

Force F₂ is 50 N, shared moment M = 10 N·m. You compute 20 × 0.5 = F₂ × 0.2, so F₂ = 10 / 0.2.

Which units do I type?

Forces F₁ and F₂ [N], arms r₁ and r₂ [m]. Force result in newtons, moment M [N·m]. Type a centimetre as 0.01.

How many fields do I fill?

Exactly three. The calculator computes the fourth plus the shared M. Two filled fields are not enough.

Is typed 0 the unknown?

No. Zero in a force is zero newtons. The unknown is one blank field, not a typed zero.

Do angled forces work here?

The model assumes 90°. Angled forces go through the torque page as M = F r sinα. There is no angle field here.

What if arm r₂ is 0 m?

That is the fulcrum. The arm must be positive, otherwise the calculator cannot divide by r₂.

Does a comma in 0.5 work?

Yes. 0.5 and 0,5 are the same r [m]. A comma and a period mean the same value.

How is this different from torque?

There one M = F r sinα. Here a two-sided lever balance at 90°: F₁ r₁ = F₂ r₂.

What F₁ at F₂ = 50 N, r₂ = 0.2 m and r₁ = 0.5 m?

Force F₁ is 20 N. That is 50 × 0.2 / 0.5. Inverse of the first example.

What r₂ at F₁ = 20 N, r₁ = 0.5 m and F₂ = 50 N?

Arm r₂ is 0.2 m. That is 20 × 0.5 / 50. Same balance, different unknown.

Knowledge sources

The formula is the school one. Units follow SI; NIST SP 330 and BIPM define the measures, not your result.

Page updated in 2026.