How To Calculate Pulley Ratio
By The Calcumatix Team Reviewed by Calcumatix Editorial Review 3 min read
Quick Answer
To calculate the pulley ratio, divide the diameter of the driven pulley (the one receiving power) by the diameter of the driver pulley (the one attached to the motor). For example, if a motor has a 4-inch driver pulley connected to an 8-inch driven pulley, divide 8 by 4 to get a ratio of 2:1. This means the driver pulley must complete two full revolutions to turn the larger driven pulley one time. Consequently, the driven pulley will spin at exactly half the speed (RPM) of the motor.
When you connect two pulleys with a belt, they rarely spin at the same speed. The motor driving the system usually spins too fast or too slow for the machinery it is powering. To correct this, engineers use different sized pulleys to either multiply the speed or reduce the speed (gearing down) of the system. The exact relationship between the size of the pulleys and the speed they spin is called the pulley ratio. This guide explains the fundamental math behind the pulley ratio and how to calculate exactly how fast your driven pulley will spin. To skip the manual math, use the pulley calculator to get the result instantly.
What Is The Speed And Diameter Pulley Formula?
The mathematics governing a two-pulley system rely on a simple inverse relationship. Assuming the belt does not slip, the product of the driver pulley’s diameter and its speed is exactly equal to the product of the driven pulley’s diameter and its speed. The core pulley equation: Driver Diameter × Driver RPM = Driven Diameter × Driven RPM.
Because of this inverse relationship, making the driven pulley larger makes it spin slower. Making the driven pulley smaller makes it spin faster. If you know three of these variables (which is usually the case when you are designing a system with a known motor), you can rearrange the formula to find the missing fourth variable using basic algebra.
To find the driven speed (RPM): Driven RPM = (Driver Diameter × Driver RPM) / Driven Diameter. To find the required driven diameter: Driven Diameter = (Driver Diameter × Driver RPM) / Target Driven RPM. Both of these formulas are simply variations of the core diameter and speed relationship.
The Step-By-Step Pulley Ratio Calculation Procedure
Whether you are building a custom bandsaw, repairing a drill press, or modifying an alternator drive, the procedure for determining your final output speed is identical. You simply need to gather your physical measurements and apply the speed and diameter formulas correctly.
Step by step:
- Measure the outside diameter of the driver pulley (the one attached to the power source) in inches.
- Measure the outside diameter of the driven pulley (the one doing the work) in inches.
- Divide the driven diameter by the driver diameter to find the physical pulley ratio.
- Identify the speed of the motor attached to the driver pulley in Revolutions Per Minute (RPM). This is usually stamped on the motor’s nameplate.
- Divide the driver RPM by the pulley ratio calculated in step 3.
- The result is the exact RPM of the driven pulley.
Worked example: Inputs: You have a 1,750 RPM electric motor with a 3-inch driver pulley. It is connected by a v-belt to a 9-inch driven pulley on a fan. Step 1 (driver size): 3 inches. Step 2 (driven size): 9 inches. Step 3 (ratio): 9 / 3 = 3 (a 3:1 ratio).
Step 4 (driver speed): 1,750 RPM. Step 5 (divide speed): 1,750 / 3 = 583.33.
Result: 583 RPM output speed (rounded to nearest whole number). Because the driven pulley is three times larger than the driver, it spins exactly three times slower. By calculating this ratio, you ensure your equipment operates at the correct speed. Explore the Calcumatix engineering calculators for related tools.
Sources and References
Frequently asked questions
How does this differ from mechanical advantage?
The pulley ratio (or speed ratio) simply dictates how fast the wheels turn based on their physical diameters. Mechanical advantage refers to the multiplication of physical force. If you have a block-and-tackle system with multiple ropes lifting a heavy weight, you are calculating mechanical advantage, not a simple diameter-based speed ratio.
Does the length of the drive belt change the pulley ratio?
No. The length of the v-belt or serpentine belt has absolutely no effect on the speed ratio. The belt only serves to transmit the rotational energy from one wheel to the other. Only the physical diameters of the two pulleys determine the ratio.
What happens if I have three pulleys in a row?
If a single belt wraps around a driver pulley and two different driven pulleys (like the serpentine belt on a car engine), you calculate the ratio for each driven pulley independently. The driver pulley dictates the speed of the belt, and each driven component (alternator, water pump, power steering) turns at its own specific RPM based on its individual diameter.
Should I measure the inside or outside diameter of a V-belt pulley?
For highly precise engineering calculations, you should measure the "pitch diameter," which is the point where the center of the v-belt rides inside the groove of the sheave. However, for most basic shop calculations and DIY projects, measuring the outside diameter of the pulley provides an estimate that is accurate enough for general use.
How do I calculate the ratio if I am gearing up instead of down?
The math is identical. If your driver pulley is 6 inches and your driven pulley is 2 inches, the ratio is 2 / 6, or 0.33. If the motor spins at 1,000 RPM, you divide 1,000 by 0.33 to get 3,030 RPM. A smaller driven pulley always spins faster than the motor.