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Pulley Ratio Calculator

The Pulley Ratio Calculator determines speed and torque relationships between driver and driven pulleys. Enter pulley diameters to find the speed ratio, output RPM, and torque multiplication for belt-driven machinery, HVAC systems, and industrial equipment.

Pulley Ratio Calculator — Live Preview
Speed Ratio
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Proportion Solver
A : B = C : D — Enter any 3 values
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Results
Visual ratio breakdown
Solved Proportion
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Simplified
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Percentages
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Decimal
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Fraction
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Visual Ratio
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    Ratio Simplifier
    Reduce any ratio to its simplest form
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    Simplified Result
    Reduced to lowest terms
    Simplified Ratio
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    GCD Used
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    Percentages
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    Decimal Ratio
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    Fraction
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    Visual Ratio
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      Ratio Scaler
      Multiply a ratio by a scale factor
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      Scaled Result
      Ratio after scaling
      Scaled Ratio
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      Original
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      Factor
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      Percentages
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      Simplified
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      Visual Ratio
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        What is a Pulley Ratio?

        A pulley ratio is the relationship between the diameters (or number of grooves) of two pulleys connected by a belt. When a small pulley drives a larger one, the output speed decreases but torque increases. A 4-inch driver pulley turning a 12-inch driven pulley creates a 3:1 ratio — speed is reduced by 3× and torque is multiplied by 3×.

        Pulley ratios are used in industrial machinery, automotive accessory drives, HVAC blower systems, drill presses, and exercise equipment. Variable-speed pulleys allow infinite ratio adjustment by changing the effective diameter.

        Formulas & Equations Used

        This Pulley Ratio Calculator uses the following core equations:

        1 Pulley Speed Ratio ▼
        Speed Ratio = Driver Diameter / Driven Diameter

        6-inch driver and 12-inch driven: Ratio = 6/12 = 1:2 (speed halved, torque doubled).

        2 Output RPM ▼
        Driven RPM = Driver RPM × (Driver Diameter / Driven Diameter)

        Motor at 1750 RPM with 3" driver and 9" driven: Output = 1750 × (3/9) = 583 RPM.

        3 Torque Output ▼
        Output Torque = Input Torque × (Driven Diameter / Driver Diameter)

        10 ft-lb input with 2:1 ratio: Output = 10 × 2 = 20 ft-lb (minus belt losses).

        How to Use This Pulley Ratio Calculator

        Follow these 3 simple steps:

        1

        Enter Your Values

        Type the known values into the input fields above. The Pulley Ratio Calculator accepts any positive numbers.

        2

        Choose Calculation Mode

        Select Solve, Simplify, or Scale mode in the calculator. Each applies different equations to your inputs.

        3

        View Results

        Click Calculate to see your answer with a visual ratio bar, pie chart, and step-by-step solution breakdown.

        Example Problems & Step-by-Step Solutions

        Here are 3 worked examples using this Pulley Ratio Calculator:

        Example 1 Motor: 1750 RPM, 4" driver, 10" driven pulley
        1 Speed Ratio = 4/10 = 0.4 (2.5:1 reduction)
        2 Output RPM = 1750 × 0.4 = 700 RPM
        3 Torque multiplied by 2.5×
        ✓ Output: 700 RPM with 2.5× torque increase
        Example 2 Find driver pulley size for 500 RPM output from 1200 RPM motor
        1 Driven pulley: 8 inches
        2 Driver = Driven × (Target RPM / Motor RPM)
        3 Driver = 8 × (500/1200) = 3.33 inches
        ✓ Use a 3.33-inch driver pulley
        Example 3 Two-stage pulley system: 3:1 then 2:1
        1 Overall ratio = 3 × 2 = 6:1
        2 Motor at 3600 RPM → output = 3600/6 = 600 RPM
        3 Torque multiplied 6×
        ✓ Final output: 600 RPM with 6× torque

        Frequently Asked Questions

        How does pulley size affect speed? ▼

        A larger driven pulley reduces output speed but increases torque. A smaller driven pulley increases speed but reduces torque. The ratio is directly proportional to the diameter ratio of the two pulleys.

        Do V-belts slip and affect the ratio? ▼

        Well-tensioned V-belts have minimal slip (1-3%). For precise applications, use timing belts (cogged/synchronous belts) which have zero slip and maintain exact speed ratios.

        Can I use different sized pulleys to save energy? ▼

        Matching pulley ratios to the required load speed improves efficiency. Running a fan at 75% speed (using pulley ratio) reduces power consumption by about 58% due to the fan affinity laws (power ∝ speed³).

        What is a variable speed pulley? ▼

        A variable speed pulley (VP) has adjustable halves that change the effective diameter. As the halves spread apart, the belt rides lower, changing the ratio. This allows continuous speed adjustment without changing pulleys.

        How do I calculate belt length for two pulleys? ▼

        Belt Length ≈ 2C + π(D+d)/2 + (D-d)²/(4C), where C = center distance, D = large pulley diameter, d = small pulley diameter. Add 1-2% for tensioning.

        Learn About Ratios

        What is a ratio?

        A ratio is a comparison between two or more quantities showing the relative size of one to another. Written as A : B, it means 'for every A units of the first quantity, there are B units of the second.' For example, a ratio of 3 : 4 means for every 3 parts of A, there are 4 parts of B. Ratios are used in cooking, construction, finance, science, and everyday life.

        How do I solve a proportion?

        A proportion is an equation that says two ratios are equal: A : B = C : D. To solve for a missing value, use cross-multiplication. If D is unknown: D = (B × C) / A. This works because in equal ratios, the cross products are always equal: A × D = B × C. Our Proportion Solver does this automatically — just enter any 3 values and it finds the 4th.

        How do I simplify a ratio?

        To simplify a ratio, find the Greatest Common Divisor (GCD) of both numbers and divide each by it. For example, 24 : 36 — the GCD of 24 and 36 is 12. So 24 ÷ 12 = 2 and 36 ÷ 12 = 3, giving the simplified ratio 2 : 3. Our Simplifier automatically finds the GCD and reduces your ratio to its lowest terms.

        What is ratio scaling and when is it useful?

        Scaling a ratio means multiplying both parts by the same factor to create an equivalent, larger (or smaller) ratio. For instance, scaling 2 : 5 by a factor of 3 gives 6 : 15. This is extremely useful for recipes (tripling a recipe), construction (scaling blueprints), mixing solutions, or any scenario where you need to maintain the same proportion at a different magnitude.

        What's the difference between a ratio and a fraction?

        A ratio A : B compares two quantities to each other (part-to-part), while a fraction A/B typically represents a part-to-whole relationship. However, any ratio can be expressed as a fraction: 3 : 4 is equivalent to 3/4 = 0.75. The key difference is context — ratios compare quantities side-by-side, while fractions represent a portion of a total.