RPM Calculator – Calculate Rotational Speed and Gear Ratios

Calculate RPM for pulley systems, gear trains, and AC motors instantly. Enter your parameters to find output speed, gear ratio, and motor synchronous speed — free online RPM calculator for engineers and mechanics.

N₂ = N₁ × (D₁ / D₂)

Driver Diameter

Driven Diameter

Driver RPM

How to Use This RPM Calculator

Select your calculation mode

Choose Pulley for belt drives, Gear for gear trains, or Motor for AC motor speed calculations.

Enter your parameters

Input driver/driven diameters for pulleys, tooth counts for gears, or frequency/poles for motors.

Calculate output speed

Click Calculate RPM to see the output speed and gear ratio. Results appear instantly below.

Common Motor Synchronous Speeds

Poles	50 Hz Sync RPM	60 Hz Sync RPM	Typical Application
2	3000	3600	High-speed pumps, compressors
4	1500	1800	General purpose motors
6	1000	1200	Fans, blowers, conveyors
8	750	900	Low-speed applications
10	600	720	High-torque drives
12	500	600	Very low-speed equipment

Note: Actual motor speed is lower than synchronous speed due to slip. Typical slip is 2-5% for induction motors.

Understanding RPM Calculations

RPM (revolutions per minute) measures rotational speed. In mechanical systems, you often need to change speed between input and output. Pulleys and gears accomplish this through ratios — a small driver turning a large driven wheel reduces speed but increases torque.

For pulley systems, the formula is N₂ = N₁ × (D₁ / D₂). If a 4-inch driver at 1000 RPM drives an 8-inch pulley, output speed is 1000 × (4/8) = 500 RPM. The larger driven pulley turns half as fast but with twice the torque. Gear systems work identically, substituting tooth count for diameter.

AC motor speed depends on electrical frequency and magnetic poles. The synchronous speed formula is 120f/p, where f is frequency in Hz and p is pole count. A 4-pole motor on 60 Hz power has a synchronous speed of 120 × 60 / 4 = 1800 RPM. Induction motors run slightly slower due to slip — typically 2-5% below synchronous speed.

Key principle: Speed reduction always increases torque proportionally (minus efficiency losses). Halving the RPM roughly doubles the available torque. This trade-off is fundamental to mechanical power transmission.

Tips for RPM System Design

Match speeds to application requirements

Different applications need different speeds. Pumps and fans often run at motor speed (1750-3450 RPM). Conveyors typically need 50-200 RPM. Gearboxes or belt reductions bridge the gap between motor output and load requirements.

Consider belt speed for pulley systems

Belt speed = π × diameter × RPM. High belt speeds cause wear and heat. V-belts typically max out around 6500 feet per minute. For a 4-inch pulley at 3600 RPM, belt speed is about 3770 FPM — acceptable for most V-belts.

Account for slip in belt drives

Belts slip 1-3% under load, reducing actual output speed slightly. Chain and gear drives have minimal slip. For precision speed requirements, use timing belts, chains, or gears instead of friction belts.

Check center distance constraints

Pulley center distance affects belt wrap angle and life. Too close reduces wrap on the small pulley, causing slip. Too far creates belt whip. A good rule: center distance should be 1-1.5 times the large pulley diameter.

Frequently Asked Questions

What is the RPM formula for pulleys?

Output RPM = Input RPM × (Driver Diameter / Driven Diameter). A smaller driver turning a larger driven pulley reduces speed. Double the driven diameter and you halve the output RPM while doubling torque.

How do I calculate gear ratio?

Gear ratio = Driven Teeth / Driver Teeth. A 40-tooth gear driven by a 20-tooth gear has a 2:1 ratio. Output speed is half the input speed, and torque doubles (ignoring efficiency losses).

Why does my motor run slower than synchronous speed?

Induction motors require slip to produce torque. The rotating magnetic field induces current in the rotor, which requires a speed difference. Typical full-load slip is 2-5%. A 4-pole 60 Hz motor syncs at 1800 RPM but runs around 1725-1750 RPM under load.

Can I use this for metric pulleys?

Yes. The ratio calculation works with any consistent units. Whether you use inches, millimeters, or tooth count, the ratio D₁/D₂ or T₁/T₂ gives the same result. Just keep both measurements in the same units.

What happens if I swap driver and driven?

Swapping reverses the ratio. If a 4-inch driver and 8-inch driven gives 2:1 reduction, swapping to 8-inch driver and 4-inch driven gives 1:2 increase — output speed doubles but torque halves. This is called "overdrive."

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