Tension Force Calculator
Find the tension in a rope, cable or string for a hanging or accelerating mass, a rope at an angle, two ropes at different angles, an Atwood pulley or a block pulled up an incline, with a diagram and worked steps.
Tension is the pull a rope transmits.
Use the Tension Force Calculator
Looking for bicycle spoke tension? Use the spoke tension calculator, or the spoke length calculator to size spokes from rim ERD.
Setup
0° = rope hangs straight down. 90° = rope is horizontal (not supported).
The angle each rope makes with a vertical line through the load. 0° = both ropes straight up.
Measured from the horizontal ceiling (left rope 1, right rope 2). 90° = straight up.
Rope parallel to the slope, pulling the block up it; μ is the kinetic friction coefficient (0 = frictionless).
0 = at rest or constant speed. Positive = accelerating upward (lifting), negative = downward.
Diagram
Result
Step-by-Step Breakdown
Enter values and click Calculate to see tension results.
Tension Formulas by Setup
Ideal rope and pulley; m = mass, g = 9.81 m/s², a = acceleration
| Setup | Tension |
|---|---|
| Hanging at rest | T = mg |
| Lifted / lowered with acceleration a | T = m(g + a) |
| One rope at θ from vertical | T = mg / cos θ |
| Symmetric Y-split, half-angle θ | T = mg / (2 cos θ) |
| Two ropes at α₁, α₂ from horizontal | T₁ = mg cos α₂ / sin(α₁+α₂), T₂ = mg cos α₁ / sin(α₁+α₂) |
| Atwood machine (m₁, m₂ over a pulley) | T = 2m₁m₂g / (m₁+m₂), a = (m₁−m₂)g / (m₁+m₂) |
| Pulled up an incline θ, friction μ | T = m(g sin θ + μg cos θ + a) |
| Horizontal pull on a level surface | T = m(a + μg) |
Quick answer
Tension is the pull a rope transmits. A mass hanging at rest: T = mg. Accelerating up or down: T = m(g + a). One rope at angle θ from vertical: T = mg ÷ cos θ. Two ropes at angles α₁ and α₂ from the ceiling: T₁ = mg·cos α₂ ÷ sin(α₁ + α₂). Atwood pulley: T = 2m₁m₂g ÷ (m₁ + m₂). Up an incline: T = m(g sin θ + μg cos θ + a).
Examples
| Setup (g = 9.81 m/s²) | Tension |
|---|---|
| 10 kg hanging at rest | 98.1 N |
| 10 kg lifted with a = 2 m/s² | 118.1 N |
| 10 kg, ropes at 30° and 60° from ceiling | 49.05 N and 84.96 N |
| Atwood pulley, 5 kg and 3 kg | 36.79 N |
| 10 kg up a 30° incline, μ = 0.2 | 66.04 N |
Pick a setup, enter the mass and angles, and get the tension with a free-body diagram and step-by-step working.
Summary
The Tension Force Calculator solves the five classic rope-tension problems from physics class and rigging: one rope (vertical or angled, with optional acceleration), a symmetric two-rope Y-split, two ropes at different angles from the ceiling, an Atwood machine (two masses over a pulley) and a block pulled up an incline with friction. Enter the mass in kg or lb and the angles; the tool shows tension in newtons and pound-force, a free-body diagram and every equation step. Ropes and pulleys are treated as ideal (massless, inextensible, frictionless pulley).
How it works
- Pick the setup: Single Rope, Two-Rope Y-Split, Two Angles, Pulley (Atwood) or Incline.
- Enter the mass in kg or lb (for the pulley, both masses).
- Single rope and Y-split: enter the angle from vertical and, optionally, a vertical acceleration (positive = upward).
- Two angles: enter each rope's angle measured from the horizontal ceiling; the tool solves both tensions from ΣFx = 0 and ΣFy = 0.
- Incline: enter the slope angle, the friction coefficient μ and any acceleration up the slope; the rope is assumed parallel to the incline.
- Click Calculate to see tension in N and lbf, the force diagram and each equation step.
Use cases
- Solve physics homework on tension in strings, ropes and cables (equilibrium and Newton's second law).
- Find the tension in each rope when a sign, lamp or load hangs from two anchors at unequal angles.
- Check the Atwood machine tension and acceleration for two masses over a pulley.
- Estimate the pull needed to drag or winch a load up a ramp with friction.
- Get a first estimate of sling or rigging leg loads before checking a rated working-load chart.