Rope Tension Calculator — Physics Force
Find the tension in a rope or cable holding a mass at a given angle from horizontal. Specify the mass, rope angle, and any upward acceleration — the calculator applies Newton's second law to return the tension and its horizontal and vertical components.
kg
°
m/s²
Tension force in the rope supporting the hanging mass
- 1
Effective load m(g + a)
5 × (9.81 + 0) = 49.05Net downward force the rope must oppose. - 2
sin(θ)
sin(90°) = 1 - 3
Tension T = m(g + a) ÷ sin θ
49.05 ÷ 1 = 49.05
How does this calculator work?
T = m(g + a) / sin(θ), where m is mass (kg), g = 9.81 m/s², a is upward acceleration (m/s², 0 if stationary), and θ is the rope angle from horizontal (90° = vertical). A 5 kg mass on a vertical rope at rest gives T = 5 × 9.81 = 49.1 N. Shallow angles greatly amplify tension.
Formula
How this is calculated
When a mass hangs from a rope inclined at angle θ from horizontal, Newton's second law in the vertical direction gives T sin(θ) = m(g + a), where g = 9.81 m/s² is gravitational acceleration and a is any additional upward acceleration. Rearranging yields T = m(g + a) / sin(θ). The horizontal tension component Tₓ = T cos(θ) must be balanced by a second rope, a wall, or another reaction force for the object to remain in static equilibrium.
For a perfectly vertical rope (θ = 90°), sin(90°) = 1 and the formula reduces to the familiar elevator equation T = m(g + a). A positive a — an elevator accelerating upward or a mass being lifted — increases tension beyond the object's weight. A negative a (decelerating upward, or accelerating downward) reduces tension. At a = −g the mass is in free fall and tension is zero.
As the rope angle decreases toward 0° (horizontal), sin(θ) → 0 and tension → infinity. This is why it is physically impossible to support any weight with a perfectly horizontal rope. The calculator assumes a massless, inextensible rope in uniform acceleration; it does not account for the rope's own weight or dynamic oscillation.
Frequently asked questions
As θ approaches 0° (horizontal rope), sin(θ) → 0 and tension T = m(g+a)/sin(θ) → infinity. In practice, any rope pulled nearly horizontal will snap or stretch rather than remain truly horizontal under load. You always need a nonzero vertical component to counteract gravity.
The tension in the cable holding you (or a scale reading) is T = m(g + a). Accelerating upward (a > 0) makes you feel heavier; decelerating upward or accelerating downward (a < 0) makes you feel lighter. In free fall (a = −9.81 m/s²), T = 0 — weightlessness.
For short, light ropes the massless rope assumption introduces negligible error. For long cables — suspension bridge cables, elevator hoisting cables, or power transmission lines — the rope's self-weight adds significantly to the tension at the attachment point and must be modelled with catenary equations instead.
Also known as
TG we-Calculate Editorial Team. (2026). Rope Tension Calculator — Physics Force [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/tension-calculator
TG we-Calculate Editorial Team. "Rope Tension Calculator — Physics Force." TG we-Calculate. 2026. https://we-calculate.com/calculator/tension-calculator.
TG we-Calculate Editorial Team, "Rope Tension Calculator — Physics Force," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/tension-calculator
@misc{wecalculate_tension_calculator, title = {Rope Tension Calculator — Physics Force}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/tension-calculator}}, year = {2026}, note = {TG we-Calculate} }
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