Tension is the pulling force transmitted through a rope, cable or chain. Lifts, cranes, suspension bridges and hanging signs are all designed around the tensions in their cables – which can be much larger than the weight they hold when the cables are nearly horizontal.
How to use the Tension Calculator
- Scenario
- Object’s mass m
- Upward acceleration a
- Angle of rope 1 from horizontal α
- Angle of rope 2 from horizontal β
- Mass m₁
- Mass m₂
- Gravitational acceleration g
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the scenario. Angles of the two ropes are measured from the horizontal. For a single rope, a positive acceleration means the object is accelerating upward.
Inputs explained
| Field | What to enter |
|---|---|
| Scenario | Choose one: Object hanging from one rope (with vertical acceleration), Object hanging from two ropes, Two masses over a pulley (Atwood machine) |
| Object’s mass m | Units: kg, g, mg, t, lb, oz |
| Upward acceleration a | Units: m/s², ft/s², g, cm/s² |
| Angle of rope 1 from horizontal α | Units: °, rad, arcmin, arcsec, mrad |
| Angle of rope 2 from horizontal β | Units: °, rad, arcmin, arcsec, mrad |
| Mass m₁ | Units: kg, g, mg, t, lb, oz |
| Mass m₂ | Units: kg, g, mg, t, lb, oz |
| Gravitational acceleration g | Units: m/s², ft/s², g, cm/s² |
What each result means
- Tension in rope 2 = [Object’s mass m]×[Gravitational acceleration g]×cos(rad([Angle of rope 1 from horizontal α]))÷sin(rad([Angle of rope 1 from horizontal α] + [Angle of rope 2 from horizontal β]))
- Weight = [Object’s mass m]×[Gravitational acceleration g]
- Acceleration of the masses = abs([Mass m₂] – [Mass m₁])×[Gravitational acceleration g]÷([Mass m₁] + [Mass m₂])
Example values
How the main result changes when Object’s mass m changes and everything else stays at the example values above:
| Object’s mass m (kg) | Tension in the rope (N) |
|---|---|
| 5 | 35.8948 |
| 7.5 | 53.8422 |
| 10 | 71.7897 |
| 12.5 | 89.7371 |
| 15 | 107.6845 |
| 20 | 143.5793 |
Formula
One rope: T = m(g + a) · Two ropes: T₁ = W·cos β / sin(α + β), T₂ = W·cos α / sin(α + β)
Atwood: T = 2m₁m₂g / (m₁ + m₂)
Worked example
Inputs — Scenario: Object hanging from two ropes; Object's mass m: 10 kg; Angle of rope 1 from horizontal α: 30 °; Angle of rope 2 from horizontal β: 45 °; Gravitational acceleration g: 9.80665 m/s².
Results — Tension in the rope = 71.7897 N; Tension in rope 2 = 87.924 N; Weight = 98.0665 N.
Key terms
- Tension
- The pulling force in a rope or cable.
Frequently asked questions
Why is tension larger when ropes are nearly horizontal?
Only the vertical components support the weight, so the total tension must grow.
Is tension the same along a rope?
For a light rope over a frictionless pulley, yes.
What is an Atwood machine?
Two masses connected over a pulley, used to study acceleration.
How do I size a rope?
Use the maximum tension with a safety factor and the rope's rated working load.