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Torque Equilibrium Calculator

Check whether moments about a pivot balance, and find the force needed for equilibrium.

About Torque Equilibrium Calculator

A lever balances when the moments about the pivot are equal, which is why a small force at a long distance holds a large force at a short one. Solving for the balancing force is a single division. Moment balance is the basis of every crane, beam and cantilever check, and it is what determines tipping loads.

Formula

Torque Equilibrium

Equilibrium requires Σ(F × d) = 0 about the pivot

moment
Force times perpendicular distance from the pivot

Worked example

With the default values below, Torque Equilibrium Calculator returns Net Torque About the Pivot of 150.000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Force on side oneminimum 0 N
500 N
Distance from the pivotminimum 0 m
1.5 m
Force on side twominimum 0 N
300 N
Distance from the pivotminimum 0.01 m
2 m

Results

Net Torque About the Pivot
150.000 N m
Moment on Side One
750.000 N m
Moment on Side Two
600.000 N m
Force on Side Two That Would Balance It
375.000 N
Status
Rotates toward side one

Step by step

  1. 1Values used
  2. 2Torque Equilibrium
  3. 3Net Torque About the Pivot= 150.000 N m
  4. 4Moment on Side One= 750.000 N m
  5. 5Moment on Side Two= 600.000 N m
  6. 6Force on Side Two That Would Balance It= 375.000 N
  7. 7Status= Rotates toward side one

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Torque Equilibrium calculated?

Equilibrium requires Σ(F × d) = 0 about the pivot A lever balances when the moments about the pivot are equal, which is why a small force at a long distance holds a large force at a short one. Solving for the balancing force is a single division.

Why does Torque Equilibrium matter?

Moment balance is the basis of every crane, beam and cantilever check, and it is what determines tipping loads.

What values do I need to enter?

This calculator takes 4 inputs: Force on side one, Distance from the pivot, Force on side two, Distance from the pivot. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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