How to Calculate Counterbalance Weights

Whenever you turn a door handle, you apply a force as though the handle were a lever. This rotational force, known as torque, lets you move weights with one weight balancing the other at both ends of the lever. You can find this method of balancing and counterbalancing in many applications from construction cranes to pushing doors open, and, using the equation for torque you can determine the force of the weight and the distance along the lever needed.

Torque Equation

Every lever, with its weights to balance and counterbalance different forces, relies on a fulcrum, the point at which the arms of the lever meet. The fulcrum should lie between both weights on either end of the lever such that the rotational force can occur.

These levers let you apply a weight to both ends such that the weights counterbalance each other. The torque, also called the moment or moment of force, lets you compare the distance and force between the two weights of the lever.

Fulcrum Weight Balance Formula

The product of the weight's force and the distance at which it's located on the arm of the lever equals that of the weight on the other side. Mathematically the fulcrum weight balance formula is Fe × de = Fl × dl for the effort force Fe, its distance to the fulcrum de, load force Fd and its distance to the fulcrum dl.

The load force and effort force describe the weights on either side of the lever, and they counterbalance each other. This means you can use the load and effort forces as weights and counterbalance weights in these applications.

If you know the angle "theta" θ between the lever of the arm and the direction of the force on the weight, you can include it in the fulcrum weight balance calculator to write torque as torque "tau" τ = F × r sin_θ_. This angle makes sure that the force is applied in the appropriate direction alongside the lever arms.

Fulcrum Weight Balance Calculator

The units for force and distance should match up for both sides of the equation. If you use pounds to measure the weight of the force, remember to convert it to newtons to get the actual force. You can use the conversion that 0.454 kilograms equals 1 pound or that 4.45 newtons equals 1 pound.

Make sure you measure the distance from the object on the lever's arm to the fulcrum. This fulcrum distance calculator lets you compare the weights a crane or forklift would use in lifting heavy weights.

Mobile Crane Counterweight Calculation

Imagine a mobile crane were lifting a steel girder that weighed one ton, or 2,000 pounds, at 50 feet with a counterweight located 20 feet on the other side of the fulcrum. The forces are applied at 90° angles to each arm of the crane's lever. Calculate the counterweight's weight that the mobile crane could use at this distance.

Because the forces are applied at 90° angles, the sin_θ_ component would equal sin_(90°), or 1. Using the equation, _Fe × de = Fl × dl, the torque for the weight, or effort force, is then 2,000 pounds times 50 feet, or 100,000 pound-feet for the weight. The counterbalance weight, or load force, is then, 100,000 pound-feet divided by 20 feet, or 5,000 pounds.

When the forces on either end of the lever are equal, the lever is at equilibrium. At equilibrium, the net force is zero, and there is no additional acceleration in the system. You can set the sum of the forces on a mobile crane or forklift equal to zero when the system is no longer accelerating or decelerating.


About the Author

S. Hussain Ather is a Master's student in Science Communications the University of California, Santa Cruz. After studying physics and philosophy as an undergraduate at Indiana University-Bloomington, he worked as a scientist at the National Institutes of Health for two years. He primarily performs research in and write about neuroscience and philosophy, however, his interests span ethics, policy, and other areas relevant to science.