How to use the cable tension calculator
- Enter the hanging load as a force. The tensions come out in the same unit.
- Choose Cable angles to enter the angle of each cable above horizontal, or Span and sag to enter the distance between the supports and the sag.
- For span and sag, also enter the position of the load from the left support.
- Read the tension in each cable, the horizontal pull on each support, the vertical share carried and the largest tension compared with the load.
Formula
Horizontal balance: T1 x cos(a1) = T2 x cos(a2)
Vertical balance: T1 x sin(a1) + T2 x sin(a2) = load
T1 = load x cos(a2) / sin(a1 + a2), and T2 = load x cos(a1) / sin(a1 + a2)
For span and sag, the angles come from the sag divided by each horizontal distance
The flatter the cables, the larger the tension. As an angle gets small the sine becomes small, so the tension grows without a simple limit.
A 100 N load on two 30 degree cables
With both cables at 30 degrees above horizontal, each carries half of the 100 N vertically, which is 50 N. The tension in each is 50 / sin(30 degrees) = 100 N, so the largest tension is 1 times the load. The horizontal pull on each support is 100 x cos(30 degrees) = 86.6025 N.
At 45 degrees and 60 degrees the cables are unequal and the steeper one carries more of the vertical load. For a 10 m span with a sag of 0.5 m and the load at the middle, the cable angle is about 5.7 degrees and the tension is roughly 5 times the load.
Why shallow cables pull so hard
A cable carries the load by its vertical component, and that is only the tension times the sine of its angle. At 30 degrees the tension equals the load. At 10 degrees it is nearly three times the load, and at 5 degrees it is about six times. Hooks, anchors and the cable itself must be rated for the tension, not for the load.
Keep a margin well above the calculated tension, and use hardware rated for the loads. For the beam or rail that the cables hang from, see the shear and moment diagram calculator and the beam deflection calculator.
What the page leaves out
The page treats a single point load hung from two light cables and ignores the weight of the cables. A long cable sags under its own weight and then forms a curve, which needs a different calculation. Cables also stretch and change length with temperature. For that see the thermal expansion calculator.
Assumptions and limits
- The load is a single point load hung from two straight cables that meet at the load.
- The weight and stretch of the cables are ignored, and the supports do not move.
- Angles are between 1 and 89 degrees above horizontal.
- The page is for estimates only. Safety critical rigging needs rated hardware and a qualified person.
Frequently asked questions
How do I find the tension in two cables?
Balance the forces. The horizontal parts of the tensions must be equal, and the vertical parts must add up to the load. The formula on the page solves both.
Why is the tension larger than the load?
A cable at a shallow angle carries only a small vertical part of its tension, so it has to pull much harder along its length to hold the load up.
What is sag?
It is how far the load hangs below the line between the supports. A small sag over a long span means shallow cables and a very large tension.
Can the cables have different angles?
Yes. Enter each angle. The steeper cable carries a larger share of the vertical load, and the horizontal pull is the same on both.