Tension per rope
For two symmetric ropes this is the force in each rope.
Physics · Forces & momentum
Rope tension calculator
Calculate tension for one hanging mass at rest, vertical acceleration, or two symmetric supporting ropes. In the two-rope mode the result is tension in each rope.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
Results
Relation and numerical substitution
T = m × g—
Massless, inextensible ropes; point mass; symmetric supports in the two-rope case. Acceleration is positive upward.
01Formulas and symbols
Formulas used
T
T = m × gFor two symmetric ropes this is the force in each rope.T
T = m × (g + a)For two symmetric ropes this is the force in each rope.T
T = m × g / (2 × sin(θ))For two symmetric ropes this is the force in each rope.02Assumptions and limits
Scope of validity
- Massless, inextensible ropes; point mass; symmetric supports in the two-rope case. Acceleration is positive upward.
03Validation example
Reference numerical case
- At m = 10 kg and g = 9.80665 m/s², T = 98.0665 N at rest. Two ropes at 30° give T = 98.0665/(2 × 0.5) = 98.0665 N each.
04References
Technical references
- University Physics 1, §6.1 Newton’s laws — OpenStax
FAQ
Why does a small rope angle increase tension?
Only T sin θ supports the mass vertically. Two nearly horizontal ropes need large tensions to provide mg.
What happens in free fall?
At a = −g the calculated tension is zero. The taut-rope assumption reaches its limit.
05Model and conventions
Calculate tension for one hanging mass at rest, vertical acceleration, or two symmetric supporting ropes. In the two-rope mode the result is tension in each rope.
06Limits of this model
No pulleys, elasticity, distributed rope weight or multi-mass dynamics. Acceleration below −g would require a rope to push and is rejected.
07Common mistakes
The angle is measured from horizontal, not vertical. Near horizontal, tension grows without bound: this is not a strength or safety rating.