Gear and Gear Train Calculator

⚙️ Gear type:

Number of teeth — pinion z₁

Number of teeth — gear z₂

Module m, mm

Helix angle β, °

Gear ratio u

Input speed n₁, RPM

Motor power P, kW

Transmission efficiency %

Center distance a, mm

Pinion diameter d₁, mm

Gear wheel diameter d₂, mm

Want a fast, no-nonsense gear simulator that actually helps you design and check gear trains? Type the known values, pick the gear type, and the app fills in the rest. It handles spur, helical, bevel and worm drives, updates ratios and speeds instantly, and gives clear outputs you can use for prototyping or teaching. This tool is perfect for quick validation before CAD or shop work.

Table of Contents

What this gear calculator does

Select drive type: spur, helical, bevel or worm
Enter tooth counts, diametral pitch or module, shaft speed and engine power
Let the simulator compute gear ratio, driven speed and angular velocities
Include efficiency to get realistic output torque and delivered power
See animated gear interaction and direction of rotation
Export a plain text report with all calculated parameters for records

Interface elements and how to use them

Field	What it sets
Drive type	Choose spur, helical, bevel or worm
z1, z2	Number of teeth on driver and driven gears
DP	Diametral pitch in inches inverse, sets pitch diameter
Helix angle	Tooth helix angle for helical gears
n1	Input speed of driver shaft in revolutions per minute
Power	Engine or motor input in horsepower
Efficiency	Transmission efficiency used for torque and output power
Animation	Visualize rotation and mesh behavior

Core formulas used

Gear ratio: u = z2 / z1
Driven speed: n2 = n1 / u (RPM)
Angular speed: omega = 2 * pi * n / 60 (rad/s)
Torque (imperial): T (lb·ft) = HP * 5252 / n
Torque (SI): T (N·m) = 9550 * P(kW) / n
Pitch diameter (in): d = z / DP
Center distance (approx): a = (d1 + d2) / 2
Helical quick correction: transverse diameter d_t ≈ d / cos(beta)

Practical examples with US numbers

Example A. Spur gear pair

Inputs: z1 = 20, DP = 8, u = 2.5, n1 = 1800 RPM, Pin = 5 HP, efficiency = 0.95
z2 = 50
Pitch diameters: d1 = 20 / 8 = 2.50 in, d2 = 50 / 8 = 6.25 in
Center distance a = (2.50 + 6.25) / 2 = 4.375 in
Driven speed n2 = 1800 / 2.5 = 720 RPM
Output power Pout = 5 * 0.95 = 4.75 HP
Output torque T2 = (4.75 * 5252) / 720 ≈ 34.65 lb·ft
Angular speeds: omega1 ≈ 188.50 rad/s, omega2 ≈ 75.40 rad/s

Example B. Helical gear

Inputs: z1 = 16, z2 = 40, DP = 8, helix angle beta = 20°, n1 = 3600 RPM, Pin = 7.5 HP, efficiency = 0.92
Spur pitch diameters: d1_spur = 16 / 8 = 2.00 in, d2_spur = 40 / 8 = 5.00 in
Transverse approx: d1 ≈ 2.00 / cos20° ≈ 2.13 in, d2 ≈ 5.00 / cos20° ≈ 5.32 in
Center distance a ≈ (2.13 + 5.32) / 2 ≈ 3.73 in
Ratio u = 2.5 → n2 = 3600 / 2.5 = 1440 RPM
Pout = 7.5 * 0.92 = 6.90 HP
T2 = (6.90 * 5252) / 1440 ≈ 25.17 lb·ft

Example C. Bevel gear

Inputs: z1 = 24, z2 = 48, DP = 6, n1 = 1200 RPM, Pin = 6 HP, efficiency = 0.93
Pitch diameters: d1 = 24 / 6 = 4.00 in, d2 = 48 / 6 = 8.00 in
Approx center distance a = (4.00 + 8.00) / 2 = 6.00 in (cone geometry required for detailed design)
n2 = 1200 / 2 = 600 RPM
Pout = 6 * 0.93 = 5.58 HP
T2 = (5.58 * 5252) / 600 ≈ 48.84 lb·ft

Example D. Worm drive

Inputs: worm starts z1 = 1, wheel z2 = 40, DP = 6, n1 = 1800 RPM, Pin = 3.5 HP, efficiency = 0.75
Ratio u = 40
Wheel pitch diameter d2 = 40 / 6 ≈ 6.667 in
Driven speed n2 = 1800 / 40 = 45 RPM
Pout = 3.5 * 0.75 = 2.625 HP
T2 = (2.625 * 5252) / 45 ≈ 306.37 lb·ft

Note: worm geometry, lead and thermal effects require detailed checks; torque above is based on output power and speed

Recommended parameter ranges

Parameter	Suggested range	Why it matters
Teeth per gear	12 to 150	Low tooth counts can cut under the root and cause interference
Diametral pitch	4 to 20	Sets tooth size and strength
Helix angle	0 to 35 degrees	Trade off noise and strength
Ratio per stage	1 to 20	Keep extreme ratios for multiple stages
Shaft speed	10 to 6000 RPM	Match speed to bearing and lubrication limits

Quick design tips that save time

Use diametral pitch that matches stocked cutter sets to avoid custom tooling
Limit single stage ratios to maintain tooth strength and avoid undercut
Account for service factor in power and torque calculations
For helical gears balance helix direction to control thrust loads
For worm drives assume lower efficiency and factor that into thermal and loading checks
Always check contact patterns in detailed design with proper geometry software before production

What to export and hand off

Save a plain text report with z1 z2 DP pitch diameters center distance ratio speeds torques and efficiency
Capture the animated mesh as an MP4 or GIF for presentations
Provide pitch diameter and key seat dimensions to the shop for cutting and blank preparation

This gear simulator gives fast and useful answers so you can iterate concepts quickly. Use it to check ratios, confirm speeds and estimate torque before moving to detailed modeling or ordering parts. A quick pre-check here avoids costly surprises later in the build process.