# Tension Calculator

URL: https://speedycalculator.com/calculators/physics/tension/
Last updated: 2026-10-30

> The tension calculator finds the tension in a rope holding a hanging or accelerating object, in two ropes supporting a weight at different angles, or in the string of an Atwood machine (two masses over a pulley).

## Inputs

- Scenario
- Object's mass m (kg, g, mg, t, lb, oz)
- Upward acceleration a (m/s², ft/s², g, cm/s²)
- Angle of rope 1 from horizontal α (°, rad, arcmin, arcsec, mrad)
- Angle of rope 2 from horizontal β (°, rad, arcmin, arcsec, mrad)
- Mass m₁ (kg, g, mg, t, lb, oz)
- Mass m₂ (kg, g, mg, t, lb, oz)
- Gravitational acceleration g (m/s², ft/s², g, cm/s²)

## Results

- Tension in the rope
- Tension in rope 2
- Weight
- Acceleration of the masses

## 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)
```

## Explanation

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

FieldWhat to enterScenarioChoose one: Object hanging from one rope (with vertical acceleration), Object hanging from two ropes, Two masses over a pulley (Atwood machine)Object's mass mUnits: kg, g, mg, t, lb, ozUpward acceleration aUnits: m/s², ft/s², g, cm/s²Angle of rope 1 from horizontal αUnits: °, rad, arcmin, arcsec, mradAngle of rope 2 from horizontal βUnits: °, rad, arcmin, arcsec, mradMass m₁Units: kg, g, mg, t, lb, ozMass m₂Units: kg, g, mg, t, lb, ozGravitational acceleration gUnits: 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)535.89487.553.84221071.789712.589.737115107.684520143.5793

## 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.

## FAQ

**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.


## Sources

- [OpenStax – University Physics Volume 1](https://openstax.org/details/books/university-physics-volume-1)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)