Tension is the pulling force a rope, cable, or string carries when something tugs on both ends. This calculator covers three classic physics scenarios — a hanging weight, a load held by two angled ropes, and an Atwood machine — so students, hobbyists, and anyone rigging a load can check the math quickly.
How the Tension Calculator works
Each scenario applies Newton's laws to a rope or cable in a specific setup. For a single vertical rope holding a stationary mass, tension simply equals weight: T = mg. For two ropes supporting a weight at different angles, the calculator solves two simultaneous equilibrium equations — one balancing the horizontal components of each rope's tension, and one balancing the vertical components against the total weight. For an Atwood machine, two masses hang from opposite ends of a rope over a pulley; because they're connected by an inextensible rope, both masses share the same magnitude of acceleration, and the tension works out to a value between the two individual weights.
All three formulas assume idealized conditions: ropes and cables are massless and don't stretch, and any pulley is frictionless and massless. Real-world ropes and pulleys introduce small losses that this calculator does not model.
Inputs and what they mean
Mass is always entered in kilograms. For the Two Ropes tab, each angle is measured from the horizontal in degrees, and must be strictly between 0° and 90° — an angle of exactly 0° (a perfectly horizontal rope) or 90° (perfectly vertical) creates a degenerate case that the equilibrium equations can't solve for a general setup. For the Atwood tab, both masses must be greater than zero; if the two masses are equal, the system is balanced and the acceleration is zero.
The angle each rope makes with the horizontal has an outsized effect on how the load is split between the two ropes: the rope closer to vertical ends up carrying most of the tension, since a nearly vertical rope behaves like a single rope holding the full weight straight down. The rope closer to horizontal contributes little vertical support and carries much less tension, even though it's still needed to balance the other rope's horizontal pull. Small changes in angle near the extremes (close to 0° or 90°) can swing the result dramatically.
Limits and edge cases
This calculator assumes massless ropes/cables and, for the Atwood scenario, a frictionless and massless pulley — real ropes have some weight and real pulleys have some friction and rotational inertia, both of which would change the numbers slightly in practice. It also assumes static equilibrium for the Hanging and Two Ropes tabs (nothing is swinging or accelerating) and standard Earth gravity (9.81 m/s²).
For more complex rigging — three or more ropes, non-planar angles, moving loads, or systems with friction — consult a structural or mechanical engineer rather than relying on this simplified model.