Case 1
- Velocity (m/s)
- 10m/s
- Radius (m)
- 2m
50.000m/s²
Open with these valuesCentripetal Acceleration Calculator
50.000m/s²
Result: 50.000 m/s²Divide the speed squared by the radius: 10 m/s on a 2 m circle gives 50 m/s². The acceleration points at the centre and changes only the direction of the motion, never the speed. Doubling the speed quadruples it; halving the radius doubles it.
Worked examples
Case 2
- Velocity (m/s)
- 20m/s
- Radius (m)
- 5m
80.000m/s²
Open with these valuesCase 3
- Velocity (m/s)
- 0.5m/s
- Radius (m)
- 0.25m
1.000m/s²
Open with these valuesHow it's calculated
a = v² ÷ r
- StepEnter the speed along the circle in metres per second — divide km/h by 3.6.
- StepEnter the radius of the circular path in metres.
- ResultRead the inward acceleration in m/s²; Earth's gravity is about 9.81 m/s².
Reference table
| v (m/s), r (m) | What it describes | a (m/s²) |
|---|---|---|
| 0.5, 0.25 | A slow turn on a tiny circle | 1 |
| 1, 1 | One metre per second, one metre out | 1 |
| 3, 9 | Jogging pace on a wide bend | 1 |
| 5, 10 | Cyclist easing round a corner | 2.5 |
| 10, 2 | Ball on a 2 m string | 50 |
| 20, 5 | Fast lap of a small track | 80 |
Questions
How do I calculate centripetal acceleration?
Divide the velocity squared by the radius of the circular path: a = v² ÷ r. Use metres per second for the velocity and metres for the radius to get metres per second squared. An object at 10 m/s on a circle of radius 2 m has 10² ÷ 2 = 50 m/s².
What is centripetal acceleration?
It is the acceleration that points toward the centre of a circle and continuously changes the direction of a moving object so it follows a curved path. Even at constant speed, an object going in a circle is always accelerating, because its direction keeps changing. It is measured in metres per second squared.
Why does a tighter circle increase the acceleration?
Because the radius sits in the denominator of a = v² ÷ r. A smaller radius means a sharper turn, so the direction must change faster, which demands more acceleration. Halving the radius doubles the centripetal acceleration at the same speed.
How is this different from centripetal force?
Centripetal acceleration describes how quickly the direction of the velocity changes, in m/s². Centripetal force is the inward push or pull, in newtons, that produces it: F = m × a = m × v² ÷ r. Multiply this acceleration by the object's mass to get the force.
Does centripetal acceleration change the object's speed?
No, it is always perpendicular to the motion, so it changes only the direction of the velocity, not its magnitude. An object can travel a circle at a perfectly steady speed and still accelerate the whole time. Acceleration measures any change in velocity, including a change in direction.
Sources and last check
Information, not professional advice.