How to use this calculator

Enter the weight of the hanging load and the angle of each cable measured up from the horizontal: α₁ for the cable going up to the left, α₂ for the one going up to the right. The calculator balances the forces at the knot where the cables meet. A cable hanging straight up is 90°.

Formulas

Equilibrium of the knotT₁ cos α₁ = T₂ cos α₂ T₁ sin α₁ + T₂ sin α₂ = W

Solved for the tensionsT₁ = W cos α₂sin(α₁ + α₂) T₂ = W cos α₁sin(α₁ + α₂)

The same answer comes from Lami’s theorem, which says each of three forces in equilibrium is proportional to the sine of the angle between the other two.

Worked example

A 1 kN load on cables at 30° and 45° (the default)

sin(30° + 45°) = sin 75° = 0.9659.
T₁ = 1000 × cos 45° / 0.9659 = 707.1 / 0.9659 = 732.1 N.
T₂ = 1000 × cos 30° / 0.9659 = 866.0 / 0.9659 = 896.6 N.
Check: 732.1 sin 30° + 896.6 sin 45° = 366.0 + 634.0 = 1000 N, and both cables pull sideways with 634.0 N.

Why shallow cables are dangerous

When both cables are at the same angle α, each carries W/(2 sin α). At 60° that is 0.58W, at 30° it is exactly W, at 15° it is 1.93W and at 5° it is 5.7W. Riggers call this sling angle loss: a sling rated for the full load can fail when it is spread wide. That is also why a clothesline or power line can never be pulled perfectly straight; the tension would be infinite.

Assumptions and limits

The cables are weightless, straight and joined at a single point with the load. Heavy cables sag into a catenary instead.
Cables can only pull. Both angles are measured up from the horizontal, between 0° and 90°.
Two vertical cables (both at 90°) make the problem statically indeterminate: how they share the load depends on their stretch.

Frequently asked questions

Which cable carries more?

The steeper one. It is closer to vertical, so it is more directly in line with the weight.

Can the tension be larger than the weight?

Yes, whenever the cables are spread wide. The sideways pulls cancel each other but still load the cables.

How do I handle a sign hanging from two points at different heights?

Measure each cable’s angle from the horizontal at the knot. The heights of the anchors only matter through those angles.