Lever and mechanical advantage calculator
Lever balance: the force on the second arm and the advantage gained.
Fill in the fields and the result will appear here automatically.
Solves the balance of two opposing torques on an ideal massless lever. d₁ and d₂ are positive perpendicular distances from the pivot to the force lines, not necessarily distances along the bar. F₁ is the input force and F₂ the output; geometric advantage d₁/d₂ can exceed or fall below one. The pivot supplies force balance, but its reaction is not calculated here.
How it works
Formula and logic
For opposing torques, F₁d₁ = F₂d₂. Thus F₂ = F₁d₁/d₂ or d₂ = F₁d₁/F₂. For non-zero forces, ideal geometric advantage F₂/F₁ = d₁/d₂. When both forces are zero, the displayed ratio describes only geometry, not 0/0.
Example
F₁ = 100 N, d₁ = 2 m and d₂ = 0.5 m give F₂ = 400 N, torque 200 N·m and advantage 4. The reverse mode with 400 N gives d₂ = 0.5 m. F₁ = 0 with positive specified arms gives F₂ = 0; it cannot balance a non-zero F₂ at a positive arm.
Fields and units
- What to find — list option
- Force on the first arm — N
- First arm — m
- Second arm — m
- Force on the second arm — N
How to use
- — Choose output force F₂ or arm d₂; the computed field does not require input.
- — Enter non-negative F₁ in N and a positive perpendicular arm d₁ in m.
- — For F₂, enter d₂ > 0; for d₂, enter F₂ > 0 and F₁ > 0.
- — Check that the forces produce opposing torques; lever weight, pivot friction and additional torques are excluded.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: force balance and opposing torques OpenStax: arm to the force’s line of action
- Limitation
- Ideal massless lever with two opposing torques and positive arms; friction, pivot reaction, strength and additional loads are not calculated.
FAQ
How is lever balance different from one force’s torque?
One torque uses its force and arm. This tool equates the magnitudes of two opposing torques; the pivot must also provide force equilibrium.
Does a lever create energy?
An ideal lossless lever trades force for displacement: more output force comes with less output displacement. Real friction and deformation reduce transmitted work.
Where and how are the arms measured?
Perpendicularly from the pivot to each force’s line of action. With an angled force the arm is shorter than the application-point distance; do not multiply a known perpendicular arm by sine again.
What if both forces act on the same side of the pivot?
They can balance if their directions produce opposing torques, as in a second-class lever. Being on one side does not by itself determine torque sign.
Are the lever’s weight and zero-force cases included?
Lever weight is excluded; its torque and any extra forces need a full equilibrium model. With F₁ = 0 and non-zero F₂, the inverse formula yields a zero arm, outside the positive-arm model.