Block and tackle calculator: pulling force and rope length
This block and tackle calculator uses the rule from OpenStax Physics: the ideal mechanical advantage of a pulley system equals the number N of rope segments supporting the load. Example: 100 kg on a block and tackle with 4 supporting ropes needs 245.17 N of pull without friction – the weight of 25.00 kg – but you pull 8 m of rope to lift it 2 m.
Example: Mass of the load 100 kg · Supporting rope segments N 4 · Efficiency 100 % · Lifting height 2 m → Pulling force: Pulling force 245.17 N (≈ 25.00 kg). Source: OpenStax Physics, 9.3 Simple Machines: IMA of a pulley system = number of ropes supporting the load (N); to raise a load 1 m you pull N m of rope; IMA = F_r/F_e = d_e/d_r; efficiency = W_o/W_i (read 09.10.2026). Updated: .
How it is calculated
Pulling force = weight of the load ÷ number of supporting rope segments. OpenStax: for pulleys, simply count the ropes supporting the load – that number N is the ideal mechanical advantage. In return you pull N times as much rope as the load rises, so the work F · d stays the same. With friction, the efficiency η is added: force = m · g ÷ (N · η).
Examples (g = 9.80665 m/s²)
| Load | N | Efficiency | Pulling force | Rope for the lift |
|---|---|---|---|---|
| 60 kg (fixed pulley) | 1 | 100 % | 588.40 N | 1 m for 1 m |
| 50 kg (movable pulley) | 2 | 100 % | 245.17 N | 2 m for 1 m |
| 100 kg | 4 | 100 % | 245.17 N | 8 m for 2 m |
| 100 kg | 4 | 85 % | 288.43 N | 8 m for 2 m |
| 200 kg | 6 | 90 % | 363.21 N | 18 m for 3 m |
Counting the ropes
Only the rope segments that hold the moving block (and so the load) count. A single fixed pulley just changes direction (N = 1); a movable pulley halves the force (N = 2). A block and tackle with two sheaves at the top and two at the bottom has N = 4. If the rope end is tied to the lower block, one more segment carries the load. The weight alone comes from the force calculator, and pounds from kg to lbs.
Frequently asked questions
How do you calculate a block and tackle?
Force = m · g ÷ N. 100 kg weigh 980.665 N; with 4 supporting ropes that is 245.17 N, the weight of 25.00 kg.
How much rope do I have to pull?
N times the lifting height: with 4 supporting ropes you pull 8 m of rope to lift 2 m.
What do a fixed and a movable pulley do?
A fixed pulley only changes direction, the force stays the same (60 kg: 588.40 N). A movable pulley shares the load between two segments and halves the force.
How do I include friction?
With the efficiency: force = m · g ÷ (N · η). At 85 % the example rises from 245.17 N to 288.43 N.
How do I count the supporting ropes?
Count the segments between the upper and lower block that hold the load. The rope you pull counts only if it leaves the lower block going upwards.
Is the result exact?
It is a calculated ideal value; in practice the weight of the lower block and the rope adds to it. Without manufacturer data the efficiency is only an estimate.
Sources and legal basis
- OpenStax Physics, 9.3 Simple Machines: IMA of a pulley system = number of ropes supporting the load (N); to raise a load 1 m you pull N m of rope; IMA = F_r/F_e = d_e/d_r; efficiency = W_o/W_i (read 09.10.2026)
- NIST SP 811, Appendix B.8 – standard acceleration of gravity g_n = 9.806 65 m/s² (read 09.10.2026)
As of: · Editorial policy
Related tools
- Force CalculatorForce calculator in newtons: from mass and acceleration, weight, pressure and area, spring constant or the lever law – with unit conversion and working.
- kg to lbs converterConvert kg to lbs and back: 1 kg = 2.2046 lb. Shows pounds and ounces, stone and pounds, grams, tons and a kg to lbs chart – exact to the legal definition.
- Gear Ratio CalculatorGear ratio calculator for gears, belts and chains: output speed and torque from tooth counts or diameters, including two-stage drives. Free, no sign-up.
- Normal Force CalculatorNormal force calculator from mass, slope angle and gravity, optionally with extra force and friction: normal force, force down the slope, friction.
- Online CalculatorCalculator online, free and instant: type or tap and see the answer as you go – order of operations, brackets, percent, square root, steps and a history list.
- School Year Calculator (England, Scotland, Northern Ireland)School year calculator for the UK: enter a date of birth and see the year group and key stage for any school year – England, Scotland and Northern Ireland.
- Beta Distribution CalculatorBeta distribution calculator: enter α, β and x to get the density, the CDF P(X ≤ x), mean, median, mode, variance, skewness and any quantile.
- Earthquake magnitude calculator: how much stronger?Earthquake magnitude calculator: compare two magnitudes – energy ratio (about 32 times per step, 1000 times for two) and amplitude ratio (10 times per step).
- Arrhenius equation calculatorArrhenius equation calculator: find activation energy from two rate constants at two temperatures, or the new k – with the formula and a worked example.