Lever Calculator: F1 d1 = F2 d2

A lever or see-saw in balance: force times distance on each side of the pivot.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • F_1d_1 = F_2d_2
  • F_2 = \frac{F_1d_1}{d_2}
  • d_2 = \frac{F_1d_1}{F_2}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the force on side 2 (the load or the effort): force on side 2 (the load or the effort) = (force on side 1 x distance of force 1 from the pivot) / (distance of force 2 from the pivot)
  2. Put the values in (every value in its SI unit): force on side 2 (the load or the effort) = (200 x 1.5) / (0.5)
  3. The answer: force on side 2 (the load or the effort): 600 N
  4. The same answer in other units: 0.6 kN; 61.183 kgf

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What is the principle of moments?

For a body in balance, the total clockwise moment about a pivot equals the total anticlockwise moment.

How do I find the force needed to lift a load with a lever?

Multiply the load by its distance from the pivot and divide by the distance of the effort from the pivot.

What is the mechanical advantage of a lever?

The effort arm divided by the load arm.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any school physics text (moments and levers).

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