Calculation
F = m·g / n
Each supporting strand shares load ideally; friction increases real pull force.
F = m·g/n
Pulley Mechanical Advantage Calculator
Each supporting strand shares load ideally; friction increases real pull force.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Pull force F — The ideal (frictionless) pull or drive force at the free rope end needed to hold or lift the load mass. The force actually required is somewhat higher because of friction in the pulleys and rope.
- Load mass m — The mass to be lifted or held. Source: weigh it, or take it from a datasheet/specification.
- Gravitational acceleration g — The gravitational acceleration; typical value 9.81 m/s².
- Supporting strands n — The number of rope strands actually supporting the movable (loose) pulley block – not the number of pulleys. A simple block-and-tackle with one loose pulley and two supporting strands has n = 2; each extra supporting strand halves the ideal pull force again.
Example
100 kg with two supporting strands: 490 N ideal.
Assumptions and limits
Frictionless pulley; rope weight and elasticity are excluded.
Understand Pulley Mechanical Advantage Calculator
This calculator finds a pulley system's ideal pull force from load mass and the number of supporting rope strands. It explains why a block and tackle saves no work at all, but trades force for pull distance — a principle used for centuries to trim sails on ships.
What does this quantity describe?
For an ideal, frictionless pulley system, the load's weight force is shared equally across all supporting strands: F = m·g/n. The more supporting strands n, the lower the pull force needed at the free end of the rope.
With a 4:1 block and tackle (four supporting strands), lifting the load by 1 m requires pulling 4 m of rope through your hands — force drops to a quarter, but the distance travelled quadruples. This exact principle has been used for centuries in ship rigging and tackle systems to let one person move loads far beyond their own pulling strength.
Formula and variables
F = m·g / n
F = m·g / nm = F·n / gn = m·g / F
| Symbol / input | Meaning |
|---|---|
| Pull force F | The ideal (frictionless) pull or drive force at the free rope end needed to hold or lift the load mass. The force actually required is somewhat higher because of friction in the pulleys and rope. |
| Load mass m | The mass to be lifted or held. Source: weigh it, or take it from a datasheet/specification. |
| Gravitational acceleration g | The gravitational acceleration; typical value 9.81 m/s². |
| Supporting strands n | The number of rope strands actually supporting the movable (loose) pulley block – not the number of pulleys. A simple block-and-tackle with one loose pulley and two supporting strands has n = 2; each extra supporting strand halves the ideal pull force again. |
Choose the inputs correctly
Enter two of the three quantities. Pull force requires load mass and strand count, load mass requires force and strands, strand count requires force and load mass. n is the number of rope segments actually supporting the moving pulley block, not the total number of pulleys.
How to use the calculator
Select the target quantity and enter the two known values with units. Keep in mind that real pull force runs somewhat above this ideal value due to friction in the pulleys and rope stiffness.
Worked example
Given m = 100 kg and n = 2 supporting strands, substitution gives F = 100 kg · 9.80665 m/s² / 2 ≈ 490.3 N.
Understand the result and units
An ideal pull force of 490.3 N means, with two supporting strands, only half the load's weight force (about 981 N) needs to be applied at the free rope end. In return, the rope must be pulled twice as far as the load is lifted.
Force in newtons (N), mass in kilograms (kg), gravitational acceleration g in m/s². The strand count n is a dimensionless integer.
Typical applications
Block-and-tackle systems are used in rigging, cranes and winch installations, salvage operations, and sail trimming, wherever available drive or hand force is limited.
Assumptions, limits and common mistakes
The formula describes an ideal, frictionless pulley system. Real systems need somewhat more pull force than the ideal value due to pulley friction and rope stiffness; accelerating the load also needs additional dynamic force beyond static equilibrium.
Common mistake: Do not mistake a block and tackle for a way to save energy: total work (force times distance) stays the same under ideal, loss-free conditions — a pulley system trades force purely for pull distance. Also, do not confuse n with the total number of pulleys in the system; it counts only the rope segments actually supporting the moving block.
Frequently asked questions
Does a block and tackle save energy or work?
No. Under ideal, frictionless conditions, total work performed stays the same; a block and tackle only trades less force for a longer pull distance.
How many supporting strands count for a multi-pulley block and tackle?
Only the rope segments actually supporting the moving (load-bearing) pulley block count, not the total number of pulleys installed in the system.
Why is real pull force higher than the calculated ideal value?
Because of friction in the pulley bearings and rope stiffness, which converts part of the applied force to heat instead of transferring it fully to the load.