How it works
Tension is the pulling force transmitted along a rope, cable or string when it is stretched taut. For an ideal (massless, inextensible) rope over a frictionless support, that force is the same at every point — which is why one number describes the whole rope.
For a single mass hung or lifted vertically, apply Newton's second law: the rope must support the weight (mg) and additionally supply whatever force accelerates the mass. Taking upward as positive, T = m(g + a). Hanging still (a = 0) gives simply T = mg; accelerating upward raises the tension; accelerating downward lowers it, and in true free fall (a = −g) the tension drops to zero.
This calculator assumes a vertical rope, a massless inextensible line and constant g ≈ 9.81 m/s². For two-mass pulley systems use the Atwood machine calculator, and for a rope pulling a block along a slope use the incline tension calculator.
Use it in real life
Lifts and cranes: a cable hoisting a 500 kg load that accelerates upward at 2 m/s² carries about 5,900 N — noticeably more than the 4,900 N it holds at rest. Cables are rated for the accelerating case, not just the static weight.
Climbing and rigging: a rope arrests a fall by decelerating the climber, so the peak tension far exceeds body weight — the physics reason dynamic ropes are designed to stretch and stretch the stopping time.
Elevators: the unsettling light-in-the-stomach feeling as a lift starts down is tension (and the normal force under your feet) dropping below your weight because a points downward.
Frequently asked questions
What is the tension in a rope holding a hanging weight?
For a stationary hanging mass the tension equals its weight: T = mg. A 10 kg mass gives about 98 N. Any upward or downward acceleration changes it via T = m(g + a).
Can tension be greater than the object's weight?
Yes. Whenever the mass accelerates upward, the rope must both support the weight and provide extra upward force, so T > mg. Sudden jerks and fall-arrests can produce tensions many times the static weight.
What assumptions does this calculator make?
An ideal rope — massless and inextensible — pulling a single mass vertically, with g ≈ 9.81 m/s². It ignores the rope's own weight, stretch, and any friction at a pulley or support.