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How the Ratio Is Calculated

A belt-and-pulley drive is governed by one physical fact: the belt cannot stretch or compress, so its linear speed must be identical everywhere it wraps a pulley. Since linear speed equals π × diameter × RPM, that constraint forces D₁ × N₁ = D₂ × N₂ — the driver pulley's diameter times its RPM equals the driven pulley's diameter times its RPM. Rearranged, the driven speed is N₂ = N₁ × (D₁ ÷ D₂): a small driver turning a large driven pulley slows the output shaft down, and a large driver turning a small driven pulley speeds it up. The same relationship governs chain sprockets and toothed gears — substitute tooth count for diameter, since tooth pitch plays the identical geometric role.

Worked example: a motor spins a 100 mm pulley at 1750 RPM and drives a 250 mm pulley on a pump shaft: N₂ = 1750 × (100 ÷ 250) = 700 RPM, a 2.5:1 reduction. Because energy is conserved (friction losses aside), the torque delivered to that shaft rises by the same 2.5:1 factor the speed dropped by — this is the entire point of gearing down: trading RPM for torque to start a heavy load or turn slow-running equipment. Flip the pulleys (250 mm driving 100 mm) and the output would instead speed up 2.5× while torque fell by the same factor.

The tool also reports belt speed, v = π · D₁ · N₁ ÷ 60,000 m/s, since that figure — not RPM — sets belt wear and safety limits: keep classical V-belts under roughly 30 m/s and narrow-profile V-belts under roughly 40 m/s.

What to Know

• Speed and torque trade off — gearing never creates either for free. A 2.5:1 speed reduction yields roughly a 2.5:1 torque increase (minus friction losses); you cannot lower RPM and raise torque beyond what the ratio allows.
• Center distance never enters the ratio. Only the two diameters (or tooth counts) set N₂ — how far apart the shafts sit changes belt length and wrap angle, not speed.
• Chains and timing belts carry the ratio exactly, with no slip, so N₂ is as precise as your diameter/tooth data; ordinary V-belts lose roughly 1-3% to slip under load, so real output speed runs a touch below theoretical.
• Multi-stage drives multiply. Two 2:1 reductions in series give 4:1 overall — a common way to reach a large ratio without one impractically oversized pulley.
• An idler or tensioner pulley doesn't touch the math. Since it is neither the driver nor the driven member, it changes belt tension and wrap angle only — it never appears in the D₁N₁ = D₂N₂ relationship.