By Zencalcy Editorial TeamLast reviewed About us
Tension is the pulling force transmitted along a rope, cable or chain. For a single hanging object at rest it simply balances weight. In an Atwood machine — two masses over a frictionless pulley — the heavier side accelerates down and the tension ends up between the two weights.
Tension in a hanging rope or in an Atwood pulley system.
Hanging: T = m g Atwood: T = 2 m₁ m₂ g / (m₁ + m₂) Atwood: a = (m₁ − m₂) g / (m₁ + m₂)
The Atwood result assumes a massless, frictionless pulley and an inextensible string. m₁ is the heavier mass, so a is positive when it descends.
| Symbol | Meaning |
|---|---|
| T | Tension in the rope, in newtons. |
| m | Hanging mass, in kilograms. |
| m₁, m₂ | The two masses on either side of the pulley, in kilograms. |
| a | Acceleration of the Atwood system, in m/s². |
An Atwood machine with 5 kg and 3 kg masses accelerates at (5 − 3) × 9.80665 / 8 = 2.45 m/s². The tension is 2 × 5 × 3 × 9.80665 / 8 = 36.77 N, between the 29.42 N and 49.03 N weights.
Continue with the Rocket Thrust Calculator, Weight Calculator, or the Apparent Weight in an Elevator — or browse more dynamics tools and all physics calculators.
The heavier mass must accelerate downward, so the upward tension is less than its weight. The lighter mass accelerates upward, so the tension is greater than its weight.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
Reference material used to build and check this calculator:
Last reviewed: September 2026. See how we build and check every tool on the about page.
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Content updated: September 2026