About the Tension Calculator
This tension calculator finds the force in a rope, cable or chain for the three classic set-ups in mechanics. Choose a single hanging mass (optionally accelerating up or down, as in a lift or crane), a load suspended from two cables at any angles, or an Atwood machine with two masses over a frictionless pulley. Results are given in newtons, pound-force and kilogram-force.
It is built for physics students solving free-body diagram problems and for riggers, DIY builders and stage or event crews who want a first estimate of how hard a line is pulling. The two-cable mode shows clearly why shallow angles are dangerous: as the cables flatten towards horizontal, the tension in each can climb to many times the weight of the load.
The model assumes massless, inextensible ropes, a frictionless pulley and static (or uniformly accelerating) loads, with standard gravity 9.80665 m/s². It is an educational estimate, not a substitute for rated working-load limits and safety factors in real lifting.
With the default inputs, the tension (largest) is 98.07 N. Change any value above to recalculate instantly.
How to use the tension calculator
- 1Choose the set-up: hanging mass, two angled cables or Atwood pulley.
- 2Enter the mass (or both masses for the pulley).
- 3For a hanging mass, enter any vertical acceleration.
- 4For two cables, enter each cable’s angle from the horizontal.
- 5Read the tension in N, lbf and kgf and compare it with the load’s weight.
Formula and method
Each case comes from Newton’s second law on a free-body diagram. A hanging mass with upward acceleration a needs T − mg = ma, so T = m(g + a). For a load held by two cables, the horizontal components must cancel (T₁cos θ₁ = T₂cos θ₂) and the vertical components must add to the weight (T₁sin θ₁ + T₂sin θ₂ = mg); solving the pair gives the formulas above, with angles measured from the horizontal. With equal angles each cable carries mg / (2 sin θ).
In an Atwood machine both masses share one rope tension and one acceleration magnitude a = |m₁ − m₂|g / (m₁ + m₂); substituting back gives T = 2m₁m₂g / (m₁ + m₂), which always lies between the two weights. Ropes are taken as massless and inextensible and the pulley as frictionless and massless.
- T
- Tension (N)
- m
- Mass of the load (kg)
- g
- Standard gravity, 9.80665 m/s²
- a
- Acceleration (m/s²)
- θ₁, θ₂
- Cable angles measured from horizontal
Worked examples
10 kg mass hanging at rest
At rest the rope simply supports the weight: T = 10 × 9.80665 = 98.07 N, which is 22.05 lbf or exactly 10 kgf.
10 kg lifted with 2 m/s² upward acceleration
T = 10 × (9.80665 + 2) = 118.07 N. The extra 20 N is the net force needed to accelerate the mass upward, which is why lift cables are rated well above the static load.
20 kg sign on two cables at 30°
With symmetric cables, T = mg / (2 sin 30°) = 196.13 ÷ (2 × 0.5) = 196.13 N each — at 30° every cable carries the full weight of the sign.
50 kg load, cables at 40° and 60°
sin(100°) = 0.985. T₁ = 490.33 × cos 60° ÷ 0.985 = 248.9 N and T₂ = 490.33 × cos 40° ÷ 0.985 = 381.4 N. The steeper cable carries more of the load.
Atwood machine with 5 kg and 3 kg
a = (5 − 3) × 9.80665 ÷ 8 = 2.45 m/s² and T = 2 × 5 × 3 × 9.80665 ÷ 8 = 36.77 N, between the 29.4 N and 49.0 N weights of the two masses.
Frequently asked questions
How do you calculate tension in a rope?+
Draw a free-body diagram and apply Newton’s second law. For a mass hanging at rest, tension equals its weight, T = mg. If it accelerates upward at a, T = m(g + a); downward, T = m(g − a).
Why does tension increase at shallow cable angles?+
Only the vertical component of each cable’s tension holds up the load. As the angle from horizontal shrinks, sin θ gets small, so each cable must pull much harder: at 10° two cables each carry about 2.9 times the weight.
What is tension in an Atwood machine?+
For two masses over an ideal pulley, T = 2m₁m₂g / (m₁ + m₂). The tension is less than the heavier weight and more than the lighter one, because the system accelerates.
Is tension measured in newtons or kilograms?+
Tension is a force, so its SI unit is the newton. Riggers often quote kilogram-force or pound-force: 1 kgf = 9.80665 N and 1 lbf = 4.448 N. A 10 kgf load is a 10 kg mass hanging at rest.
Does the length of the rope affect tension?+
Not for an ideal massless rope — tension depends on the forces and angles, not the length. For long, heavy cables the rope’s own weight adds tension that grows toward the top.