Solve circular motion speed with flexible input modes. See velocity, omega, period, and frequency values. Download reports in CSV or PDF for sharing quickly.
| Radius (m) | RPM | ω (rad/s) | Linear velocity (m/s) | Frequency (Hz) | Period (s) |
|---|---|---|---|---|---|
| 0.35 | 1200 | 125.664 | 43.982 | 20.000 | 0.050 |
| 1.20 | 300 | 31.416 | 37.699 | 5.000 | 0.200 |
| 0.10 | 60 | 6.283 | 0.628 | 1.000 | 1.000 |
Linear velocity is the tangential speed of a point moving in a circle. It tells how fast the point travels along the circular path, not how fast it spins. One full revolution covers a path length of 2πr, so larger circles create more travel per turn.
The core relationship is v = r·ω. If r is 0.10 m and ω is 6.283 rad/s, the tangential speed is 0.628 m/s. Doubling the radius doubles linear velocity for the same ω, and doubling ω doubles v at the same radius.
You can express rotation rate as RPM, frequency f (Hz), or period T (s). Use ω = 2πf and f = 1/T. Many users also apply v = 2πr f and v = 2πr·RPM/60 for quick checks. A useful benchmark: 60 RPM equals 1 Hz (ω ≈ 6.283 rad/s). If you know v and r, compute ω = v/r and then RPM = 60ω/2π. This is helpful for motor selection and basic safety checks quickly.
Small lab rotors often run at 3,000–15,000 RPM. For r = 0.05 m at 10,000 RPM, ω ≈ 1047 rad/s and v ≈ 52.4 m/s. In the sample table, r = 0.35 m at 1,200 RPM gives v ≈ 44.0 m/s and f = 20 Hz.
This calculator converts radius between mm, cm, m, ft, and in, and converts speed between m/s, km/h, mph, and ft/s. Remember that 1 m/s = 3.6 km/h and ≈ 2.237 mph, so 44.0 m/s is about 158.4 km/h or 98.4 mph.
Measure radius to the point of interest, not the overall diameter. If you use diameter, divide by 2 first. RPM readings can fluctuate; averaging several readings improves stability. For very small radii, small measurement errors create large percentage changes in v.
Compute belt and pulley surface speed, wheel rim speed, fan blade tip speed, and turntable motion. In design checks, compare v to material limits, vibration constraints, or guard requirements. Export CSV or PDF to attach calculations to reports and logs.
Linear velocity is the tangential speed along the circular path. It equals the distance traveled per second at a chosen radius, and it differs from angular rate, which describes how fast the object rotates.
It uses v = r·ω as the primary relation. It also converts between rotation measures with ω = 2πf, f = 1/T, and ω = 2π·RPM/60.
No. Provide radius plus any one of ω, RPM, frequency, or period. If you enter several, the calculator prioritizes ω, then RPM, then frequency, then period to compute the remaining values.
Points farther from the center travel a longer arc each revolution. With the same rotation rate, doubling the radius doubles the path length per turn, so tangential speed doubles as well.
Yes. Choose the target in the Solve for menu. For radius, supply linear velocity and a rotation rate. For RPM, provide ω, frequency, or period (or speed and radius) and the tool computes RPM.
The math is exact for ideal circular motion. Accuracy mainly depends on your measured radius and rotation rate, plus unit choices and rounding. Use consistent units and average unstable RPM readings for better results.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.