Enter the two hanging masses (m1 and m2) into the Atwood Machine Calculator to find the system's acceleration and string tension. Optionally set a custom gravitational acceleration for other planets. Results are based on Newton's second law applied to a frictionless, massless-pulley setup.
System Acceleration (a)
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String Tension (T)
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Weight of m₁ (W₁)
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Weight of m₂ (W₂)
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Net Force on System
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Total System Mass
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An Atwood machine is a simple device consisting of two masses connected by a string over a frictionless, massless pulley. It is used to study Newton's laws of motion and demonstrates how unequal masses accelerate under gravity. The system provides a controlled way to measure gravitational acceleration experimentally.
The acceleration is calculated using the formula a = (m₂ − m₁) × g / (m₁ + m₂), where m₁ and m₂ are the two masses and g is gravitational acceleration. The larger mass descends while the smaller mass rises, and if both masses are equal the system remains in static equilibrium with zero acceleration.
The string tension is given by T = 2 × m₁ × m₂ × g / (m₁ + m₂). This represents the force the string exerts on each mass. Because the pulley is assumed massless and frictionless, the tension is the same throughout the string.
This calculator assumes the pulley is massless and frictionless, the string is massless and inextensible, and air resistance is negligible. These are the standard simplifications used in introductory physics. In a real Atwood machine, pulley mass and friction would slightly reduce the measured acceleration.
When m₁ equals m₂, the net force on the system is zero, so the acceleration is 0 m/s². The tension in the string equals the weight of either mass (m × g), and the system remains in static equilibrium — neither mass moves.
Yes. The gravitational acceleration field defaults to 9.81 m/s² for Earth, but you can change it to any value. For example, use 1.62 m/s² for the Moon, 3.72 m/s² for Mars, or 24.79 m/s² for Jupiter to see how the acceleration and tension change in different gravitational environments.
The heavier mass experiences a greater gravitational force (weight) than the lighter mass. Since both are connected by the same string, the net unbalanced force — equal to the difference in their weights — causes the system to accelerate in the direction of the heavier mass. The acceleration is shared equally across both masses because they move as a single system.
Weight (W = m × g) is the gravitational force pulling each mass downward. Tension is the upward force the string exerts on each mass. In an accelerating Atwood machine, the tension is always between the weights of the two masses — greater than the lighter mass's weight and less than the heavier mass's weight.