Tension Force Calculator

How it works

1. 1Choose a scenario — hanging at rest, vertical acceleration, or Atwood machine — then enter the mass values.
2. 2Each input is converted to SI (kg, m/s²) before the dynamics core applies the exact tension formula for that scenario.
3. 3The result is converted back to your chosen unit system and displayed alongside the governing formula.

Use cases

• Engineering and physics homework — verify rope tensions in pulley and elevator problems.
• Rigging and lifting — estimate the load on a rope or cable supporting a stationary or accelerating object.
• Lab pre-work — predict Atwood machine behaviour (acceleration and tension) before running the experiment.

Frequently asked questions

What is the tension in a rope holding a stationary hanging mass?

T = mg, where m is the mass in kilograms and g ≈ 9.81 m/s². For example, a 5 kg mass hanging at rest gives T = 5 × 9.81 ≈ 49 N.

How does vertical acceleration affect rope tension?

T = m(g + a). When a lift accelerates upward (a > 0) the rope carries extra load, so tension rises above mg. Downward acceleration (a < 0) reduces it — in free fall (a = −g) the tension drops to zero.

What is the Atwood machine tension formula?

For two masses over a frictionless pulley: T = 2m₁m₂g ÷ (m₁ + m₂), and the acceleration is a = |m₁ − m₂|g ÷ (m₁ + m₂). With m₁ = 3 kg and m₂ = 5 kg: T ≈ 36.8 N and a ≈ 2.45 m/s².