Calculators
Atwood Machine Calculator
Calculate acceleration and rope tension for two masses on an ideal Atwood machine, privately in your browser.
Calculate the motion of two masses sharing a pulley.
An ideal Atwood machine has two hanging masses m₁ and m₂ joined by a taut, inextensible, massless rope over a massless frictionless fixed pulley. Taking downward motion of mass 2 as positive, acceleration a = g(m₂ − m₁)/(m₁ + m₂). Rope tension T = 2gm₁m₂/(m₁ + m₂), equal on both sides. For masses 3 kg and 5 kg with g = 9.80665 m/s², a = 2.4516625 m/s² and T = 36.7749375 N. The heavier mass accelerates downward; equal masses give zero acceleration and T = mg. The direction of acceleration need not be the direction of existing velocity. The default gravity is standard gravity; enter another positive value if needed. Inputs range from 1e-12 to 1e12 in SI units. This model excludes pulley inertia, axle friction, rope mass or stretch, air resistance, and contact with the floor. It applies only while both masses hang freely and the rope stays taut. Results use browser floating-point arithmetic rounded to 12 significant digits. All inputs stay on your device.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
How are acceleration and tension calculated?
With mass 2 downward positive, a = g(m₂ − m₁)/(m₁ + m₂). Tension is T = 2gm₁m₂/(m₁ + m₂). Both masses have the same acceleration magnitude and opposite directions.
What happens when the masses are equal?
Acceleration is zero and tension equals either mass multiplied by gravity. If initially at rest, the masses remain at rest; an ideal system already moving keeps constant velocity.
What is an example?
For 3 kg and 5 kg at g = 9.80665 m/s², mass 2 accelerates downward at 2.4516625 m/s² and rope tension is 36.7749375 N.
Can this include a real pulley with inertia?
No. The model assumes a frictionless massless pulley and a taut massless inextensible rope. Pulley inertia, friction and rope weight require a different model.
Which units and values should I enter?
Use kilograms for masses and m/s² for positive gravity, each from 1e-12 to 1e12. Scientific notation is accepted. All calculation happens locally in your browser.