Tension Calculator

Calculate rope or cable tension for a mass accelerating vertically.

Calculate tension force
Enter SI values. Positive acceleration is upward; use a negative value for downward acceleration.

About tension force

Tension is the pulling force transmitted through a taut rope, cable, chain, or similar connector. This calculator evaluates the common case of one mass moving vertically while supported by a lightweight rope. The governing equation is T = m(g + a), where T is tension in newtons, m is mass in kilograms, g is gravitational acceleration in meters per second squared, and a is the vertical acceleration of the load. A positive acceleration points upward. A negative acceleration points downward. For a stationary load or one moving at constant velocity, acceleration is zero and tension equals the weight mg. If the load accelerates upward, the rope must both support its weight and produce the extra upward acceleration, so tension exceeds weight. If it accelerates downward without being in free fall, tension is below weight. At a = -g, the object and rope are in free fall and this idealized equation gives zero tension. The model assumes a massless rope, no stretching, no pulley friction, and a uniform gravitational field. Engineers use tension calculations when sizing lifting cables, analyzing elevators, checking hoists, and studying introductory dynamics. The calculated force is only the ideal working force. Real designs also account for shock loading, rope mass, bends, wear, fatigue, environmental exposure, attachment strength, and an appropriate safety factor. Never select lifting hardware solely from an ideal calculator result. Use the manufacturer’s working load limit and applicable safety standards. Sign convention matters. Enter upward acceleration as positive and downward acceleration as negative, even if the object is currently moving in the opposite direction. Velocity does not determine the sign of acceleration. Earth’s standard gravitational acceleration is approximately 9.81 m/s², but local gravity varies slightly with latitude and elevation. You can change the gravity field for another location or planetary body. Keep all values in the displayed SI units so the output is directly reported in newtons.

Tension calculation examples

These examples use T = m(g + a) with g = 9.81 m/s².

InputsTensionSituation
m = 10 kg, a = 0 m/s²98.1 NStationary load
m = 25 kg, a = 2 m/s²295.25 NAccelerating upward
m = 50 kg, a = -1.5 m/s²415.5 NAccelerating downward

How to calculate tension

  1. Enter the supported mass in kilograms.
  2. Enter vertical acceleration, using a positive value upward and a negative value downward.
  3. Confirm gravitational acceleration for the location.
  4. Select Calculate tension and read the force in newtons.

Frequently asked questions

Is tension the same as weight?

Tension equals weight only when vertical acceleration is zero in this model. Upward or downward acceleration changes the force carried by the rope.

Why can acceleration be negative?

The calculator defines upward as positive, so downward acceleration is negative. This sign convention lets the same equation describe lifting and lowering.

What happens in free fall?

At a downward acceleration equal to gravity, the ideal tension is zero. The rope is no longer required to support or accelerate the falling mass.

Can I use this result to choose a cable?

The result is an ideal dynamic force, not a working load rating. Apply engineering safety factors and follow cable, rigging, and regulatory guidance.

Does rope mass affect tension?

Yes, a real rope’s weight can make tension vary along its length. This simplified calculator treats the rope as massless and reports the force at the load.