Mechanical calculator
Pulley Ratio and Speed Calculator
See how driver and driven pulley diameters change shaft speed, belt travel, and theoretical torque.
Sage’s guided lesson
Let’s understand the result before using it
Calculate pulley ratio, driven RPM, belt speed, and theoretical torque change from driver and driven pulley diameters. I’ll show you what the numbers mean, how to check the math yourself, and where real-world conditions can change the answer.
Start with the system
What this calculator is actually doing
In a simple belt drive without slip, both pulley rims move at the same linear speed. A larger driven pulley turns more slowly; a smaller driven pulley turns faster. Torque changes in the opposite direction of speed, before losses.
Mark the driver and driven pulley before entering diameters. The ratio changes direction when those roles are swapped.
Now for the arithmetic
How to do the math yourself
Driven RPM = driver RPM × driver diameter ÷ driven diameter. Ratio = driven diameter ÷ driver diameter. Belt speed in feet per minute = π × driver diameter in inches × driver RPM ÷ 12. Ideal output torque = input torque × ratio.
Worked example
A 3 in driver turns at 1,750 RPM and drives a 9 in pulley.Ratio = 9 ÷ 3 = 3:1Driven RPM = 1,750 × 3 ÷ 9 = 583.33 RPMIdeal torque is multiplied by 3 before efficiency losses.Round output speed to match the accuracy of motor speed and measured pulley pitch diameters.
I know this is off topic, but this reminds me of a joke I heard when teaching this to one of my interns, What do you call a book about horses? A stable read. Yeah, I don’t see the connection either, but I think it is cute!
Before you build, wire, mix, or run it
Tips, shortcuts, and mistakes to avoid
- Use pitch diameters when the pulley manufacturer provides them; outside diameter can produce a small ratio error.
- Allow for belt slip, flex, bearing drag, and pulley efficiency when estimating real speed and torque.
- Check the belt manufacturer’s minimum pulley diameter, wrap angle, tension, and rated speed before building the drive.
Belt slip, load, pulley groove geometry, and motor droop make actual output speed lower than the ideal calculation.
How we got here
A little history and background
Belt drives became a defining feature of early factories, where line shafts distributed power to many machines. Flat belts were followed by V belts, timing belts, and modern synchronous systems, but the basic speed relationship remains a diameter ratio.
What the result does not tell you
The result assumes no slip and ignores belt stretch, pulley groove geometry, wrap angle, tension, bearing loss, startup load, and motor speed change under load. It is not a belt selection or guarding calculation.
Frequently asked questions
Which pulley is the driver?
The driver is attached to the power source. The driven pulley receives power from the belt.
Do idler pulleys change the speed ratio?
An idler normally changes belt routing, wrap, or tension, not the basic ratio between driver and driven pulley.
Why is actual output speed lower?
Belt slip, motor speed droop, pulley tolerances, and measurement error can all reduce the real speed.
That wraps up the lesson
Class is over. It is officially cheese fries time.
You now know more about how the Pulley Ratio and Speed Calculator actually works, not just which buttons to press. That earns cheese fries, Sage’s favorite way to celebrate a finished lesson.
Use the result within its limits
Rotating belts and pulleys can pull in clothing, hair, fingers, and tools. Use suitable guards, alignment, tension, and components rated for the operating speed.