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MachineCalcs

Pulley Calculator

Pulley (sheave) ratio, driven RPM and belt surface speed for a two-pulley belt drive, from the driver and driven diameters and the driver speed. Metric and imperial.

Inputs

mm
mm
rpm

Results

Pulley ratio(i) ✓
2.5

reduction

driven ÷ driver (n:1).

Driven speed(n₂)
700 rpm

Belt speed(v)
9.163 m/s

Surface (rim) speed of the belt.

  • Ratio i = driven diameter ÷ driver diameter. Driven speed n₂ = n₁ · D₁ / D₂.
  • This drive is a reduction (driven slower than driver).
  • Belt (surface) speed v = π · D · n uses the driver pulley — the belt runs at the same surface speed on both pulleys (no slip).
  • Diameters are pitch (effective) diameters, not the outer rim; for V-belts use the pitch diameter, not the OD.

How it works

The pulley ratio is the driven pulley diameter divided by the driver pulley diameter: i = D₂ / D₁ A ratio above 1:1 is a reduction — the driven pulley turns slower than the driver. The driven speed is inversely proportional to diameter: n₂ = n₁ · D₁ / D₂.

The belt (surface) speed is how fast the belt travels along the rim: v = π · D · n. Because the belt does not slip, it runs at the same surface speed on both pulleys, so either one gives the same result — here we use the driver. Use the pitch (effective) diameter, not the outer rim.

Worked example

A 100 mm driver pulley driving a 250 mm driven pulley is a 2.5:1 reduction. At 1,750 RPM in, the driven pulley turns 1750 × 100 / 250 = 700 RPM. The belt surface speed is π × 0.1 m × (1750 / 60) ≈ 9.16 m/s. Those are the numbers the calculator shows for these inputs.

Frequently asked questions

How do I calculate pulley ratio and RPM?
The pulley ratio is the driven diameter divided by the driver diameter: ratio = D₂ / D₁. The driven speed is n₂ = n₁ · D₁ / D₂. For example a 100 mm driver and a 250 mm driven pulley is a 2.5:1 ratio, so a 1,750 RPM motor turns the driven pulley at 700 RPM.
How does pulley size change speed?
A bigger driven pulley turns slower. Speed is inversely proportional to diameter: if the driven pulley is twice the diameter of the driver, it turns at half the speed (and vice versa). Increasing the driver diameter speeds the driven pulley up.
What is belt speed (surface speed)?
Belt speed is how fast the belt travels along the pulley rim: v = π · D · n, using the driver diameter D and its speed n. Because the belt does not slip, it runs at the same surface speed on both pulleys. It is reported here in m/s (or ft/min in imperial).
How do I find the driver size for a target driven RPM?
Rearrange n₂ = n₁ · D₁ / D₂ to D₁ = D₂ · n₂ / n₁. Pick the driven pulley diameter and speed you need, then size the driver. Or, holding the driver fixed, the driven diameter is D₂ = D₁ · n₁ / n₂.
Should I use the outer diameter or the pitch diameter?
Use the pitch (effective) diameter, not the outer rim. For a V-belt the belt rides below the top of the groove, so the pitch diameter is slightly smaller than the OD; using the OD overstates the ratio.
Does this work in metric and imperial?
Yes — enter the pulley diameters in mm or inches, and belt speed is shown in m/s or ft/min. Toggle SI/Imperial in the header.

Method & assumptions

  • No belt slip — the belt runs at the same surface speed on both pulleys, so the speed ratio equals the diameter ratio.
  • Diameters are pitch (effective) diameters, not the outer rim; for a V-belt the pitch diameter is slightly smaller than the OD.
  • Ignores belt creep and the small slip of real friction (flat / V) belts; toothed (timing) belts have effectively zero slip.

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