Equilibrium Calculator

How it works

1. 1Enter up to three forces using a sign convention: positive for one direction, negative for the opposite.
2. 2The calculator sums the forces to find the resultant (net force), ΣF = F₁ + F₂ + F₃.
3. 3The equilibrant is −ΣF — the single extra force that makes the net force exactly zero.

Use cases

• Checking whether a beam or girder is in static equilibrium under multiple applied loads.
• Finding the anchor tension needed to keep a cable junction stationary under several forces.
• Teaching Newton’s first law: an object at rest needs ΣF = 0, so the equilibrant balances the resultant.

Frequently asked questions

What is static equilibrium and what does ΣF = 0 mean?

A system is in static equilibrium when it is at rest and the vector sum of all forces is zero (ΣF = 0). By Newton’s first law, zero net force means zero acceleration, so the object stays put. Along one line, the forces in the positive direction must equal those in the negative direction.

What is the difference between the resultant and the equilibrant?

The resultant is the single force equivalent to all applied forces combined (ΣF). The equilibrant is the force needed to cancel it (−ΣF) — equal in magnitude, opposite in direction. If the resultant is already 0, no equilibrant is needed.

Can you show a worked example?

For forces F₁ = 10 N (right, positive), F₂ = −4 N (left), and F₃ = 2 N (right): the resultant is 10 + (−4) + 2 = 8 N to the right. The equilibrant is −8 N — an 8 N force to the left — which brings the net force to zero.