Centripetal Acceleration Calculator With Angular Velocity

Enter radius and rotational speed in seconds. Choose units, see steps, and validate inputs easily. Download a neat report for your project records now.

Calculator

All methods compute ω, then apply a = ω²r.
Steps appear in the result panel.
Reset

Example data

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.

Formula used

a = ω²r

  • a is centripetal acceleration in m/s².
  • ω is angular velocity in rad/s.
  • r is radius in meters.

Conversions supported

  • ω(rad/s) = ω(deg/s) × π/180
  • ω(rad/s) = 2π × (rev/s)
  • ω(rad/s) = 2π × RPM / 60
  • ω = v / r when linear speed is provided
  • ω = 2π / T when period is provided
  • ω = 2πf when frequency is provided
  • g-force = a / 9.80665

How to use this calculator

  1. Select an input method that matches your data.
  2. Enter the radius and choose its unit.
  3. Provide rotational information for the chosen method.
  4. Enable steps if you want to see conversions.
  5. Press Calculate to view the result above the form.
  6. Use the CSV or PDF buttons in the result panel.

Article

1) Why centripetal acceleration matters

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.

2) How angular velocity drives the result

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.

3) Typical data points you can compare

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.

4) Working across units without mistakes

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.

5) Reading results as g-force

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.

6) Engineering checks and safe ranges

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.

7) Practical workflow for reports

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.

FAQs

1) What is centripetal acceleration?

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.

2) Which formula does this calculator use?

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.

3) Why must ω be in rad/s?

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.

4) Can I use linear speed instead of angular velocity?

Yes. Choose the linear speed method and enter v and r. The calculator computes ω = v/r and then finds a.

5) What does the g-force value mean?

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.

6) Why do my results look extremely large?

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.

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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.