Rope Tension Calculator

What Is Rope Tension?

Tension is the pulling force transmitted through a rope, cable, or string. In static or slow-moving problems, tension balances weight and other forces so the system stays in equilibrium or accelerates predictably.

Tension Formulas

Hanging weight (vertical rope):

$$T = mg$$

Mass on a frictionless incline (rope parallel to slope):

$$T = mg\sin\theta$$

Two-mass pulley (Atwood machine, ideal rope):

$$T = \frac{2 m_1 m_2 g}{m_1 + m_2}$$

Example: a 10 kg mass hanging still on Earth has tension $T = 10 \times 9.81 = 98.1$ N.

Free-Body Diagram Tips

Draw all forces on each mass. On an incline, only the component of weight along the slope ($mg\sin\theta$) is balanced by tension when there is no friction. For a pulley, both masses pull on the same rope, giving the combined formula above.

Related tools: Torque Calculator and Inclined Plane Calculator.

Frequently Asked Questions

Is tension the same at every point in a rope?

For a massless rope over an ideal pulley with no friction, yes. Real ropes and pulleys can have slight variation, but introductory problems assume uniform tension.

Why is inclined-plane tension multiplied by sin(theta)?

Only the component of weight parallel to the slope tries to slide the mass down. That component is $mg\sin\theta$, which tension opposes in equilibrium.

What is an Atwood machine?

Two masses hang from opposite sides of a pulley. The heavier mass accelerates down while the rope tension is between $m_1 g$ and $m_2 g$.

Can tension be greater than the weight?

Yes. In an accelerating Atwood machine or an elevator rising, tension can exceed the weight of one mass. Static hanging weight gives $T = mg$ exactly.

What gravity value should I use?

9.81 m/s² is standard on Earth. Change it for other planets or custom problems. The calculator lets you edit gravity directly.

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Tension Calculator

What Is Rope Tension?

Tension Formulas

Free-Body Diagram Tips

Frequently Asked Questions

Related Tools

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