Tension Calculator

Free tension calculator with full step-by-step working, real-world examples and instant answers.

T = 2m₁m₂g/(m₁+m₂)

Mass 1 (m₁) (kg)Mass 2 (m₂) (kg)

45.436N

String tension T

1.549 m/s²

System acceleration

1
Atwood machine: two masses over an ideal pulley. Net driving force is the weight difference:
a = g·|m₁ − m₂| / (m₁ + m₂) = 9.81 × 1.5 / 9.5 = 1.549 m/s²
2
Tension from either mass's equation of motion (T = m₂(g + a) for the lighter mass):
T = 2·m₁·m₂·g / (m₁ + m₂)
3
Substitute:
T = 2 × 5.5 × 4 × 9.81 / 9.5
4
Result:
T = 45.436 N
5
Sanity check: T lies between the two weights.
39.24 N < T < 53.96 N ✓

Assumes a massless, inextensible rope and frictionless, massless pulley — the standard idealization. A real pulley with rotational inertia lowers the acceleration and changes the two tensions slightly.

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Step-by-step tension calculator for students, teachers and curious minds.

About Tension Calculator

The Tension Calculator shows the full working for every calculation — every substitution and every step, exactly the way a good teacher writes it on the board. Assumes a massless, inextensible rope and frictionless, massless pulley — the standard idealization.

How to use Tension Calculator

1Enter your known values in the input fields (sensible real-world defaults are pre-filled).
2The tool recomputes the result live on every keystroke.
3Read the answer in the result box, then expand the step-by-step solution to see the full working.
4Copy the method into your notebook, or change inputs to explore how the result behaves.

Why use Tension Calculator?

✓Instant results as you type — no submit button, no waiting
✓Step-by-step solution shown for every calculation, not just the final answer
✓Realistic example values pre-loaded so you can see a worked example immediately
✓100% free, no sign-up, runs entirely in your browser — your numbers never leave your device
✓Mobile-friendly and fast enough to use mid-homework or mid-lesson

Frequently asked questions

How does the Tension Calculator work?+

It applies the standard textbook method and shows the working for your exact inputs in the steps section, so you can follow and verify every stage of the calculation rather than trusting a black box.

What should I keep in mind when using this calculator?+

Is the Tension Calculator free to use?+

Completely free, with no sign-up or limits. All computation happens client-side in your browser, so it is fast, private, and works even on slow connections once the page has loaded.

Can I use this for homework, teaching or exam prep?+

That is exactly what it is built for. The step-by-step working mirrors how solutions are presented in class, so you can check homework, build worked examples for teaching, or practise method recall before exams.

Embed Tension Calculator on your website

Want Tension Calculatoron your own site? Paste this snippet into any HTML page — it's free, with no API key or sign-up. The tool loads in an iframe and keeps working exactly as it does here.

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