Calculate the pitch line velocity of a gear from pitch diameter and RPM (v = πDN/60), or solve for pitch diameter or speed, in ft/s, ft/min, m/s and more.
Pitch Line Velocity Formula
Pitch line velocity is the tangential linear speed at the pitch circle of a rotating component. In gears, sprockets, timing drives, and similar power-transmission parts, it converts rotational speed into the actual surface speed seen at the pitch line.
- PLV = pitch line velocity in feet per second
- d = pitch diameter in inches
- w = rotational speed in revolutions per minute
This calculator can also accept other diameter and angular-speed units, then convert them to the correct internal form before solving. The most important measurement is the pitch diameter, not the outside diameter, root diameter, or radius.
Why This Equation Works
One full revolution moves a point on the pitch circle through one circumference. The circumference comes from the pitch diameter, while the rotational speed tells you how many circumferences occur each minute. The conversion factors account for inches to feet and minutes to seconds.
Unit-Aware Forms
| Typical Inputs | Formula | Output |
|---|---|---|
| Diameter in inches, speed in RPM | PLV = (π d w) / (720) |
ft/s |
| Diameter in feet, speed in revolutions per second | v = π D n |
ft/s |
| Diameter in meters, speed in RPM | v = (π d n) / (60) |
m/s |
| Radius in meters, angular speed in radians per second | v = ω r |
m/s |
Solving for a Missing Value
If you know the pitch line velocity and one other variable, the same relationship can be rearranged to solve for the missing quantity.
| Unknown | Formula |
|---|---|
| Pitch diameter in inches | d = (720 × PLV) / (π w) |
| Rotational speed in RPM | w = (720 × PLV) / (π d) |
How to Use the Calculator
- Choose pitch line velocity, pitch diameter, or rotational speed as the unknown.
- Enter the two known values with their correct units. Use pitch diameter, not radius or outside diameter.
- Select the result unit and Calculate. Inputs remain unchanged; the answer appears in the results area.
- Open Calculation details for the formula and conversions. Reset clears this calculator’s values and saved result.
Rotational speed may be entered in RPM, RPS, radians per minute, degrees per minute, or radians per second. One revolution is 2π radians or 360 degrees: divide rad/min by 2π or deg/min by 360 to obtain RPM. Linear speed uses exact length/time factors: 1 ft/s = 0.3048 m/s and 1 mph = 0.44704 m/s. Zero rotation gives zero line velocity; finding a physical diameter requires both speeds to be positive. This calculator returns speed magnitudes, not direction.
Example
If a gear has a pitch diameter of 8 inches and rotates at 40 RPM, the pitch line velocity is:
Interpretation and Common Mistakes
- Larger pitch diameter increases pitch line velocity when RPM stays the same.
- Higher RPM increases pitch line velocity when pitch diameter stays the same.
- Meshing gears share the same pitch line velocity at the point of contact, even though their rotational speeds may differ.
- Use pitch diameter only; using outside diameter will overstate the result.
- Do not substitute radius for diameter unless the equation is written in radius form.
- Pitch line velocity is not the same as tooth-tip speed; each uses a different reference circle.
Where Pitch Line Velocity Is Useful
Pitch line velocity is commonly checked when comparing gear sizes, evaluating chain and sprocket speed, estimating operating severity, reviewing lubrication requirements, and understanding how fast a drive system is moving through mesh. Because it combines size and rotational speed into a single number, it is often more informative than RPM alone.
