Enter radius and rotational speed in seconds. Choose units, see steps, and validate inputs easily. Download a neat report for your project records now.
| Radius (m) | Angular velocity (rad/s) | Centripetal acceleration (m/s²) | g-force (g) |
|---|---|---|---|
| 0.35 | 12.50 | 54.6875 | 5.576 |
| 1.20 | 8.00 | 76.8000 | 7.832 |
| 0.05 | 120.00 | 720.0000 | 73.438 |
Values are rounded for display.
a = ω²r
Centripetal acceleration describes how strongly a moving object is pulled toward a circular path’s center. It appears in vehicle cornering, rotating machinery, lab centrifuges, and rides. If you underestimate it, parts can slip, bearings overheat, or occupants experience unexpected loads.
The calculator uses a = ω²r. Because ω is squared, doubling ω makes acceleration four times larger. For example, at r = 0.35 m, increasing ω from 10 to 20 rad/s raises a from 35 to 140 m/s².
A centrifuge might run near 3,000 RPM. That is about 314 rad/s. At a 0.08 m rotor radius, the acceleration is roughly 7,900 m/s², close to 800 g. A bicycle wheel at 5 m/s with a 0.33 m radius has ω ≈ 15.15 rad/s and a ≈ 75.5 m/s². A car taking a 25 m curve at 15 m/s produces about 9 m/s², near 0.92 g.
Rotation data often comes as RPM, rev/s, or deg/s, while radii may be in cm or inches. Converting everything to rad/s and meters keeps the formula consistent. This tool converts to SI internally, then reports the acceleration and an equivalent g‑value for quick interpretation.
People and equipment limits are commonly expressed in g. Using g = a / 9.80665, 49 m/s² is about 5 g. Passenger comfort in cars is often below 0.5 g, while engineered amusement rides may briefly exceed 3 g under controlled conditions.
Use centripetal acceleration to estimate required friction, belt tension, or containment strength. A rotating arm of 1.2 m at 8 rad/s produces 76.8 m/s², around 7.8 g. That load multiplies on fasteners and joints, so conservative safety factors matter. Even small radii can be harsh: a 0.05 m rotor at 120 rad/s reaches 720 m/s².
Pick the input method you measured: ω, RPM, v, period, or frequency. Enter radius, calculate, then export CSV for spreadsheets or PDF for documentation. If you enable steps, the report records conversions, helping you reproduce results and audit assumptions later.
It is the inward acceleration required to keep motion circular. It points toward the center and depends on angular speed and radius, even when the object’s speed stays constant.
It computes angular velocity in rad/s, then applies a = ω²r. If you enter speed, period, frequency, or RPM, the tool converts those into ω first.
Radians are the SI angle unit that makes the equation dimensionally consistent. Using deg/s or RPM directly without conversion will understate acceleration by a large factor.
Yes. Choose the linear speed method and enter v and r. The calculator computes ω = v/r and then finds a.
It is the acceleration expressed as multiples of standard gravity, using a/9.80665. It helps compare loads to comfort limits, equipment ratings, and safety guidance.
High ω and small radius can create huge acceleration because ω is squared. Check units, especially RPM vs rad/s, and verify the radius is not accidentally entered in cm or mm.
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.