Calculates the tension in a rope or cable holding a mass vertically, accounting for gravity and any additional acceleration.
How it works
The mass is multiplied by the sum of standard gravity and any additional vertical acceleration to give the tension force.
What this does not include
This covers only a single vertical hanging mass — angled ropes or multi-rope systems require different, more complex equations.
How to use this calculator
- Enter the hanging mass and any additional vertical acceleration (0 for a mass at rest).
A worked example
A 5 kg mass hanging at rest (zero acceleration): tension = mass × g = 5 × 9.80665 = 49.0332 N, exactly balancing gravity.
A 10 kg mass accelerating upward at 2 m/s²: tension = mass × (g + acceleration) = 118.0665 N — more than just supporting the weight, since the rope must also provide the extra force to accelerate it.
What the variables mean
| Variable | Meaning |
|---|---|
| Mass | Mass of the hanging object |
| Acceleration | Additional acceleration beyond gravity (zero for a stationary or constant-velocity object) |
Edge cases worth knowing
At zero acceleration, tension simply equals weight — the first example is the everyday case of something hanging motionless, where tension just counteracts gravity.
A negative mass has no physical meaning, so the calculator declines to show a result for one.
Frequently asked questions
Why does tension equal weight for a mass at rest?
Because the rope must exactly balance gravity’s pull to keep the mass from falling — Newton’s first law requires the net force to be zero for an object at rest.
What happens if the mass accelerates upward?
The rope must supply extra force beyond just balancing gravity, increasing tension above the resting value.
Does the rope’s own weight matter?
This calculator assumes a massless rope, the standard simplifying assumption in introductory physics — a heavy rope would add its own weight to the tension calculation.
