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Gear Ratio Calculator

The Gear Ratio Calculator computes the mechanical advantage between meshing gears from tooth counts. Determine output RPM, torque multiplication, and overall gear train ratios for single-stage and compound systems.

Gear Ratio Calculator — Live Preview
Gear 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 Gear Ratio?

        Gear ratio is the ratio of teeth on the driven gear to teeth on the driving gear. A 60-tooth driven gear meshed with a 20-tooth driving gear creates a 3:1 ratio — the driving gear rotates 3 times for every 1 rotation of the driven gear, tripling torque while reducing speed by one-third.

        Gear ratios are fundamental in automotive transmissions, industrial gearboxes, clock mechanisms, bicycle drivetrains, and robotics. Understanding gear ratios allows engineers to match motor speed and torque to application requirements precisely.

        Formulas & Equations Used

        This Gear Ratio Calculator uses the following core equations:

        1 Gear Ratio ▼
        Gear Ratio = Driven Gear Teeth / Driving Gear Teeth

        Driven (60 teeth) / Driver (20 teeth) = 3:1 ratio.

        2 Output RPM ▼
        Output RPM = Input RPM / Gear Ratio

        Input 3600 RPM with 3:1 ratio: Output = 3600 / 3 = 1200 RPM.

        3 Compound Gear Train Ratio ▼
        Overall Ratio = Ratio₁ × Ratio₂ × ... × Ratio_n

        Two stages of 3:1 and 4:1: Overall = 3 × 4 = 12:1 total reduction.

        How to Use This Gear Ratio Calculator

        Follow these 3 simple steps:

        1

        Enter Your Values

        Type the known values into the input fields above. The Gear 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 Gear Ratio Calculator:

        Example 1 40-tooth gear driven by 10-tooth pinion
        1 Gear Ratio = 40 / 10 = 4:1
        2 Speed reduction: 4×
        3 Torque increase: 4×
        ✓ 4:1 ratio — 4× torque multiplication
        Example 2 Motor at 1800 RPM through 5:1 gearbox
        1 Output RPM = 1800 / 5 = 360 RPM
        2 Output torque = Input torque × 5
        3 If input = 10 Nm, output = 50 Nm
        ✓ Output: 360 RPM at 50 Nm torque
        Example 3 Two-stage reducer: 3:1 and 4:1
        1 Overall ratio: 3 × 4 = 12:1
        2 Motor at 3600 RPM → 3600/12 = 300 RPM
        3 Torque multiplied 12×
        ✓ 12:1 overall ratio, 300 RPM output

        Frequently Asked Questions

        What does a higher gear ratio mean? ▼

        A higher gear ratio (like 5:1 vs 2:1) means more speed reduction and more torque multiplication. The driving gear spins more times per output rotation. This is common in first gear of transmissions for starting from a stop.

        How do compound gear trains work? ▼

        Compound trains stack multiple gear pairs. Each pair's ratio is multiplied together. Three stages of 3:1 each give 3³ = 27:1 overall ratio. This allows massive speed reductions in a compact package.

        What is a gear reduction vs overdrive? ▼

        Reduction means the output is slower than input (ratio > 1). Overdrive means output is faster than input (ratio < 1). Cars use overdrive gears (like 0.75:1) for highway fuel economy.

        How do I calculate gear ratio for a specific output speed? ▼

        Gear Ratio = Input RPM / Desired Output RPM. To get 500 RPM from a 3000 RPM motor: Ratio = 3000/500 = 6:1. Then choose gear teeth: 12T driver / 72T driven = 6:1.

        Does gear ratio affect power output? ▼

        No. Power (watts) is conserved through the gear train (minus friction losses of 1-5% per stage). A 3:1 ratio multiplies torque by 3× but divides speed by 3×. Power = Torque × Speed remains constant.

        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.