Answer first
What this calculator tells you
Calculate the inward force and acceleration needed to move a mass around a curve. Check the grip a vehicle needs to hold a turn at a given speed. Formula: Centripetal acceleration = v² ÷ r; force = m × v² ÷ r. At the worked-example inputs, the centripetal force (n) is 9,600. Holding every other input steady, moving mass (kg) from 960 to 1,440 moves the result from 7,680 to 11,520.
Transparent method
The formula
Check the grip a vehicle needs to hold a turn at a given speed.
Worked example
Example inputs
How to interpret the result
Moving in a curve needs a force pointing toward the center, and the force grows with the square of the speed. A 1,200 kilogram car at 20 meters per second in a 50 meter turn needs 9,600 newtons, an acceleration of 8 meters per second squared, or about 0.8 g. Tires provide that force through friction, so a tighter curve or a higher speed can exceed what the road offers.
At the worked-example inputs the centripetal force (n) is 9,600. It rises with speed (m/s) and mass (kg) and falls as turn radius (m) increases.
These are textbook formulas for ideal conditions: no air resistance, no friction, gravity of 9.81 meters per second squared and gases that behave ideally. Real results differ, so treat them as first estimates and use the units the formulas expect (meters, kilograms, seconds).
Before you rely on it
What to check
Compare the required force with the friction available. A wet or icy road provides much less than a dry one, at the same speed.
The common error
Where people go wrong with centripetal force calculator
Treating the outward push as a real force. What you feel is inertia, and the only real force in the turn points inward toward the center.
Sensitivity evidence
How mass (kg) changes the centripetal force (n)
Holding every other input at the worked-example value, moving mass (kg) from 960 to 1,440 moves the centripetal force (n) from 7,680 to 11,520: a spread of 3,840, or 40% of the worked-example result.
| Mass (kg) | Centripetal force (N) | Centripetal acceleration (m/s²) |
|---|---|---|
| 960 | 7,680 | 8 |
| 1,080 | 8,640 | 8 |
| 1,200worked example | 9,600 | 8 |
| 1,320 | 10,560 | 8 |
| 1,440 | 11,520 | 8 |
Every input, tested
Which input moves the centripetal force (n) most
Of the 3 inputs, speed (m/s) moves the centripetal force (n) most (3,840 across the range tested) and mass (kg) moves it least (1,920).
| Input | Tested from | To | Centripetal force (N) at each end | Swing |
|---|---|---|---|---|
| Speed (m/s) | 18 | 22 | 7,776 to 11,616 | 3,840 (40%) |
| Turn radius (m) | 45 | 55 | 10,666.7 to 8,727.3 | 1,939.4 (20%) |
| Mass (kg) | 1,080 | 1,320 | 8,640 to 10,560 | 1,920 (20%) |
Two variables at once
Centripetal force (N) by mass (kg) and speed (m/s)
Across the grid the centripetal force (n) runs from 4,915.2 to 16,588.8. Moving mass (kg) from 960 to 1,440 shifts it by 3,840 at the middle column, and moving speed (m/s) from 16 to 24 shifts it by 7,680 at the middle row, so speed (m/s) is the bigger lever here.
| Mass (kg) \ Speed (m/s) | 16 | 20 | 24 |
|---|---|---|---|
| 960 | 4,915.2 | 7,680 | 11,059.2 |
| 1,080 | 5,529.6 | 8,640 | 12,441.6 |
| 1,200 | 6,144 | 9,600 | 13,824 |
| 1,320 | 6,758.4 | 10,560 | 15,206.4 |
| 1,440 | 7,372.8 | 11,520 | 16,588.8 |
The highlighted cell is the worked example: 9,600.
Step by step
The worked example, input by input
| Input | Value used | What it means |
|---|---|---|
| Mass (kg) | 1,200 | Enter the mass (kg) used in this calculation. |
| Speed (m/s) | 20 | Enter the speed (m/s) used in this calculation. |
| Turn radius (m) | 50 | Enter the turn radius (m) used in this calculation. |
| Centripetal force (N) | 9,600 | |
| Centripetal acceleration (m/s²) | 8 | |
Inputs, definitions and assumptions
Mass (kg)
Enter the mass (kg) used in this calculation. The prefilled worked-example value is 1,200.
Speed (m/s)
Enter the speed (m/s) used in this calculation. The prefilled worked-example value is 20.
Turn radius (m)
Enter the turn radius (m) used in this calculation. The prefilled worked-example value is 50.
How to use this calculator
- 1Verify the inputs. Gather mass (kg), speed (m/s) and turn radius (m) from your own documents; the prefilled values are examples.
- 2Save a baseline. The worked example puts the centripetal force (n) at 9,600. Store your own version of it as Scenario A.
- 3Test one change. Start with speed (m/s), the input with the biggest effect here: moving speed (m/s) from 18 to 22 takes the centripetal force (n) from 7,776 to 11,616, a swing of 40% of the worked-example figure.
- 4Check the extremes. At half the example speed (m/s) (10) the centripetal force (n) is 2,400; at double (40) it is 38,400.
People also ask
Frequently asked questions
How do you calculate centripetal force?
Centripetal acceleration = v² ÷ r; force = m × v² ÷ r. At the worked-example inputs the centripetal force (n) is 9,600.
What does the centripetal force result mean?
Check the grip a vehicle needs to hold a turn at a given speed. At the worked-example inputs the centripetal force (n) is 9,600. It rises with speed (m/s) and mass (kg) and falls as turn radius (m) increases.
How much does mass (kg) change the centripetal force (n)?
Holding every other input at the worked-example value, moving mass (kg) from 960 to 1,440 moves the centripetal force (n) from 7,680 to 11,520, a spread of 3,840.
What are the limits of this centripetal force calculator?
These are textbook formulas for ideal conditions: no air resistance, no friction, gravity of 9.81 meters per second squared and gases that behave ideally. Real results differ, so treat them as first estimates and use the units the formulas expect (meters, kilograms, seconds). The tables on this page test mass (kg) only from 960 to 1,440; a value outside that range is not tabulated here.
Which input moves the centripetal force (n) most in the centripetal force calculator?
Ranked by how far each moves the centripetal force (n) across the range tested: speed (m/s) (3,840, 40%), turn radius (m) (1,939.4, 20%) and mass (kg) (1,920, 20%).
If I double speed (m/s) in the centripetal force calculator, does the centripetal force (n) double?
Doubling it from 20 to 40 takes the centripetal force (n) from 9,600 to 38,400, which is 4.00 times the worked-example figure. So the result grows faster than the input does. Halving it to 10 gives 2,400.
How much does speed (m/s) matter in the centripetal force calculator?
The worked example uses 20. With the other inputs left at the worked example, moving speed (m/s) from 18 to 22 takes the centripetal force (n) from 7,776 to 11,616, a swing of 40% of the worked-example figure.
How much does turn radius (m) matter in the centripetal force calculator?
The worked example uses 50. Holding every other input at its worked-example value, moving turn radius (m) from 45 to 55 takes the centripetal force (n) from 10,666.7 to 8,727.3, a swing of 20% of the worked-example figure.
Which inputs change the centripetal acceleration (m/s²) in the centripetal force calculator?
At the worked-example inputs it is 8. Speed (m/s) takes it from 6.5 to 9.7 and turn radius (m) takes it from 8.9 to 7.3.
What is the difference between speed and velocity?
Speed is how fast something moves. Velocity is speed with a direction. A car circling a track at a steady 30 mph has a constant speed and a changing velocity, because its direction keeps changing.
Sources and evidence
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