Pitch Line Velocity Calculator

Calculate gear speed easily with our Pitch Line Velocity Calculator.

This tool helps you find how fast a gear tooth moves in a straight line. You only need two values — the pitch diameter and the angular velocity. That’s it! In seconds, you’ll get the pitch line velocity in units like ft/s, m/s, km/h, or mph.

What Is Pitch Line Velocity?

Pitch Line Velocity (PLV) tells how fast a gear’s teeth move at the pitch circle. It’s the linear speed at the gear’s pitch diameter — not the rotational speed. Imagine a bicycle gear. When it spins, the edge moves faster than the center. That edge speed is what PLV shows.

This value helps engineers match gears correctly and reduce wear. It also tells how efficiently power transfers between gears in a spur gearing system.

Pitch Line Velocity Formula

The formula to find PLV is simple and comes from Shigley’s Mechanical Engineering Design:

PLV = π × (d / 12) × (w / 60)

Where:

• PLV = Pitch Line Velocity (ft/s)
• d = Pitch diameter (inches)
• w = Angular velocity (RPM)

This means:

Multiply π by the pitch diameter (in inches) divided by 12, then multiply by the angular velocity (in RPM) divided by 60.

Example Calculation

Let’s say the pitch diameter is 8 inches, and the gear runs at 40 RPM.

PLV = 3.1416 × (8 / 12) × (40 / 60)

PLV = 3.1416 × 0.6667 × 0.6667

PLV = 1.396 ft/s

That’s the linear speed of the gear teeth.

How to Use the Pitch Line Velocity Calculator

1. Enter the pitch diameter and choose the unit (in, mm, cm, m, ft).
2. Enter the angular velocity and choose its unit (RPM, RPS, rad/s, deg/s).
3. Pick your desired output unit (ft/s, m/s, km/h, mph, or in/s).
4. Click Calculate.

You’ll instantly get the pitch line velocity along with detailed step-by-step working.

The calculator even converts units automatically, so you don’t have to worry about conversion math.

Why Pitch Line Velocity Matters

PLV helps in designing gears that run smoothly.

If the velocity is too high, friction and heat can damage the gear.

If it’s too low, the gear may not transmit enough power.

So, engineers always check PLV to balance performance and durability.

It’s also useful when you want to compare spurs, helical gears, or even belt drives.

Real-World Example

Think of a car transmission. When the engine spins at 2000 RPM, the gear teeth move at high speed. Engineers use PLV to ensure the gears can handle that speed without wearing out.

The same goes for wind turbines, bicycles, or industrial machines — wherever gears spin, PLV matters.

Final Verdict

The Pitch Line Velocity Calculator is a handy tool for anyone working with gears. It saves time, avoids conversion errors, and gives instant results. You’ll get clarity, speed, and accuracy in one simple step.

Whether you’re an engineer, student, or hobbyist, this calculator makes your gear calculations quick and reliable.

FAQs

What is the unit of pitch line velocity?

PLV is usually measured in feet per second (ft/s), but you can convert it to m/s, km/h, mph, or in/s.

What’s the difference between RPM and PLV?

RPM measures how many times a gear spins per minute, while PLV shows how fast the gear’s edge moves in a straight line.

Can I calculate PLV if my data is in mm or m/s?

Yes! The calculator handles unit conversions automatically.

What does a higher PLV mean?

A higher PLV means the gear teeth move faster — great for speed, but it can cause more wear.

Is this calculator free?

Yes! It’s free, easy to use, and works on any device.