Mechanical

Sprocket Calculator

Calculate sprocket ratio, driven RPM, chain speed, pitch diameters, and a whole-tooth driven sprocket for a target output speed.

Formula i = N2 / N1Reviewed Sep 8, 2026

A roller-chain sprocket drive sets speed ratio directly from tooth counts. The driven sprocket turns at n2 = n1 x N1 / N2, while the ratio is i = N2 / N1. This sprocket calculator focuses on chain-drive decisions: it computes ratio, driven RPM, chain pitch-line speed, pitch diameters, torque multiplier, and can suggest the nearest whole driven sprocket for a target output RPM.

Calculation Bench

Solve for

Chain Pitch

01Driver Sprocket Teeth

N1 · Input sprocket tooth count

02Driven Sprocket Teeth

N2 · Output sprocket tooth count

03Driver Speed

n1 · Input sprocket speed

04Chain Pitch

p · Pin-to-pin pitch; presets fill this field

Use driver teeth for the input sprocket and driven teeth for the output sprocket. Use Chain Length Calculator next for links and center distance.

Solution

Enter sprocket teeth, speed, and chain pitch to calculate ratio and chain speed.

i = N2 / N1

Formula Sheet

i=\dfrac{N_2}{N_1}

n_2=n_1\dfrac{N_1}{N_2}

N_2=N_1\dfrac{n_1}{n_2^*}

v=\dfrac{pN_1n_1}{60}

PD=\dfrac{p}{\sin(180^\circ/N)}

N1Driver Sprocket Teeth
N2Driven Sprocket Teeth
iSprocket Ratio
n1Driver Speed
n2Driven Speed
pChain Pitch
vChain Speed
PDPitch Diameter

Common ANSI Chain Pitch Presets

Chain	Pitch	Use case
ANSI #25	6.35 mm / 0.250 in	Small light-duty drives
ANSI #35	9.525 mm / 0.375 in	Karts, small machines, light duty
ANSI #40	12.7 mm / 0.500 in	General-purpose roller chain
ANSI #50	15.875 mm / 0.625 in	Medium-duty machinery
ANSI #60	19.05 mm / 0.750 in	Industrial and agricultural drives
ANSI #80	25.4 mm / 1.000 in	Heavy-duty power transmission

Variables & Units

Symbol	Variable	Description	Common Units
N1	Driver Sprocket Teeth	Tooth count on the input sprocket.
N2	Driven Sprocket Teeth	Tooth count on the output sprocket.
i	Sprocket Ratio	Driven teeth divided by driver teeth. Above 1 is reduction; below 1 is overdrive.
n1	Driver Speed	Rotational speed of the input sprocket.	rpm, rev/s, Hz
n2	Driven Speed	Rotational speed of the output sprocket.	rpm, rev/s, Hz
p	Chain Pitch	Distance between adjacent chain pins.	mm, in
v	Chain Speed	Linear pitch-line speed of the roller chain.	m/s, ft/min
PD	Pitch Diameter	Theoretical pitch circle diameter for a sprocket.	mm, in

How to Use This Calculator

01Choose Ratio & Speed when both sprocket tooth counts are known.
02Choose Target Output RPM when you know the driver sprocket, input speed, and desired driven speed.
03Pick a common ANSI chain pitch or enter a custom pitch; pitch is needed for chain speed and pitch diameters.
04Read the ratio verdict: reduction, overdrive, or direct drive, plus the driven RPM and chain speed.
05In Target Output RPM mode, compare the ideal tooth count with the rounded whole-tooth suggestion, then check the achieved RPM error before ordering a sprocket.
06Use the Chain Length Calculator next when you need link count and actual center distance.

How the Formula Works

For a positive roller-chain drive, the chain speed is the same at both sprockets, so rotational speed is inversely proportional to tooth count. The ratio convention here is i = N2 / N1, where N1 is the driver and N2 is the driven sprocket.

A ratio above 1 is a reduction: output speed decreases and torque is multiplied ideally by the same ratio before losses. A ratio below 1 is overdrive: output speed increases while torque is reduced.

Chain speed uses v = p N1 n1 / 60 when n1 is entered in rpm; the calculator converts other speed units before applying the same pitch-line-speed relationship.

Pitch diameter is PD = p / sin(180deg / N). It is the theoretical pitch circle the chain rollers sit on, not the outside tooth-tip diameter.

Worked Example 01

15-tooth driver and 45-tooth driven sprocket

Known

Driver sprocket: 15 teeth
Driven sprocket: 45 teeth
Driver speed: 1,000 rpm
Chain pitch: 12.7 mm

Formula

i = N2 / N1

Substitution

i = 45 / 15; n2 = 1,000 x 15 / 45; v = 12.7 mm x 15 x 1,000 / 60,000

Result

i = 3.00:1, n2 = 333 rpm, chain speed = 3.18 m/s

This is a 3:1 reduction. The output sprocket turns one-third as fast as the driver, while ideal torque is multiplied about three times before losses.

Worked Example 02

Driven sprocket for a 350 rpm target

Known

Driver sprocket: 15 teeth
Driver speed: 1,000 rpm
Target driven speed: 350 rpm

Formula

N2 = N1 n1 / n2*

Substitution

N2 = 15 x 1,000 / 350

Result

Ideal N2 = 42.86 teeth, so use 43 teeth; achieved speed is about 349 rpm

A real sprocket needs a whole tooth count. The calculator rounds to 43 teeth and shows the achieved output speed so the rounding error is visible.

Applications

01Checking output RPM for a machine, conveyor, kart, motorcycle, bicycle, or jackshaft chain drive
02Comparing sprocket changes before ordering parts
03Estimating chain pitch-line speed for lubrication and wear screening
04Finding a whole-tooth driven sprocket that comes closest to a target RPM

Assumptions

01Roller chain engages positively with no slip.
02Driver and driven sprockets use the same compatible chain pitch.
03The calculator rejects tooth counts below 3 because the pitch-diameter geometry becomes nonphysical at very low counts.
04Torque multiplier is ideal and ignores friction, bearing losses, chain efficiency, and dynamic effects.
05Target-driven-speed mode rounds the suggested sprocket to the nearest whole tooth and recomputes achieved RPM.

Where This Model Stops

01Does not calculate chain length, center distance, wrap angle, sag, or take-up travel; use the Chain Length Calculator for that step.
02Does not select chain size, horsepower rating, lubrication method, service factor, strand count, or sprocket material.
03Does not verify tooth strength, chordal action, minimum sprocket tooth count, shaft loads, bearing loads, guarding, or vehicle top speed. Very small sprockets can run rough and wear faster even when the ratio math is correct.
04Pitch diameter is theoretical; manufacturer tooth form and hub dimensions govern the actual sprocket part.

References

[1]
Sprocket Calculator
MachineCalcs
Reference for sprocket ratio, driven RPM, chain speed, pitch diameters, and target tooth-count suggestion.
[2]
Sprocket Speed Calculator
Calculator Academy
Reference for the V2 = V1 x T1 / T2 sprocket speed relation.
[3]
Sprocket Pitch Diameter
Rough Logic
Reference for PD = p / sin(180deg / N) and the pitch-diameter vs outside-diameter distinction.

Frequently Asked Questions

How do I calculate sprocket ratio?

Use i = driven teeth / driver teeth. A 45-tooth driven sprocket with a 15-tooth driver gives i = 45 / 15 = 3.0, a 3:1 reduction.

How is this different from the Gear Ratio Calculator?

The Gear Ratio Calculator handles generic tooth-count speed ratios. This Sprocket Calculator is chain-drive specific: it adds chain pitch, chain speed, sprocket pitch diameter, whole-tooth target suggestions, and chain-drive warnings.

How is this different from the Chain Length Calculator?

The Chain Length Calculator answers how many links are needed for a given center distance. This calculator answers what ratio, driven RPM, chain speed, and pitch diameters a sprocket pair produces.

What is sprocket pitch diameter?

Pitch diameter is the theoretical circle through the chain-pin centers as the chain wraps the sprocket. It is calculated as PD = p / sin(180deg / N) and is not the same as outside tooth-tip diameter.

Can I choose any whole tooth count that gives the speed I want?

Not always. The ratio may be mathematically valid, but the sprocket still needs to fit the chain standard, meet manufacturer minimum-tooth guidance, leave enough wrap, and keep chain speed and lubrication within the chain rating.

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