Use this centripetal force calculator to find the inward force, acceleration, speed, angular speed, or period for circular motion.
Advanced options
How to use our Centripetal Force Calculator
- Choose an option in Solve for to tell the calculator which quantity you want to find.
- Enter Radius (m) because radius is needed in every mode, and make sure it is greater than 0.
- Fill in the other visible inputs for your mode, such as Mass (kg), Speed (m/s), Angular speed (rad/s), Period (s), or Centripetal force (input when solving for speed, omega, or period).
- Open Advanced options if you want to change Display format, set Significant figures, or pick a Likely force source note.
- Click Calculate to show the results.
- Read the output cards: Centripetal force is the required inward net force, Centripetal acceleration is the inward acceleration, and the other cards show the matching circular-motion values.
- Use Equivalent acceleration to compare the turning acceleration with normal gravity; for example, 2 g means the centripetal acceleration is twice standard gravity.
- Sanity-check your result: if radius gets larger while speed stays the same, Centripetal acceleration and Centripetal force should get smaller, not larger.
Definitions
Solve for: The quantity the calculator will compute from the other inputs.
Centripetal force: The inward net force needed to keep an object moving in a circle, not a separate extra force by itself [1].
Centripetal acceleration: The inward acceleration present in uniform circular motion [3].
Radius (m): The distance from the center of the circle to the path of the object.
Speed (m/s): The linear or tangential speed along the circular path.
Angular speed (rad/s): How fast the angle changes; one full revolution is 2 pi radians.
Period (s): The time for one complete revolution.
Equivalent acceleration (g): Centripetal acceleration divided by standard gravity, where standard gravity is 9.80665 m/s^2 [2].
Force-source note: A plain-language reminder of which real force, such as tension, friction, normal force, or gravity, might be providing the inward net force.
Common mistakes and quick fixes
Mistake: Typing the diameter into Radius (m) .
Fix: Enter half the full width of the circle's path in Radius (m) .
Mistake: Leaving Mass (kg) blank when Solve for is set to Centripetal force .
Fix: Add a mass greater than 0 in Mass (kg) , because force depends on mass in that mode.
Mistake: Putting revolutions per second into Angular speed (rad/s) .
Fix: Convert to radians per second first, or use Period (s) if you know the time for one full turn.
Mistake: Using 0 or a negative value in Period (s) , Speed (m/s) , or Radius (m) .
Fix: Enter positive values only, because the calculator blocks zero and negative values for these circular-motion inputs.
Mistake: Entering your target force into the result card instead of Centripetal force (input when solving for speed, omega, or period) .
Fix: Switch Solve for to Speed , Angular speed , or Period , then type the known force into the input with that full label.
Mistake: Treating Force-source note as a separate added force.
Fix: Read it as an interpretation of what real force may be supplying the needed Centripetal force , not as extra force on top of it.
Limitations & Key Assumptions / Boundary Conditions
- This calculator uses SI units only: kilograms, meters, seconds, radians per second, and newtons.
- It assumes uniform circular motion, so the formulas match steady speed around a circular path.
- Radius (m) must be greater than 0 in every mode.
- Mass (kg) matters only when the selected mode needs force; hidden fields should not affect the result.
- Speed (m/s), Angular speed (rad/s), Period (s), and the force input used for solving backward must be positive when that mode requires them.
- Equivalent acceleration is just a comparison to standard gravity. It does not tell you the exact sensation a rider or object would feel in every real setup.
- Force-source note is an interpretation helper only. It does not change the math or prove which real force is acting in a specific situation.
- Real systems can differ because of friction limits, changing speed, non-circular paths, air drag, or multiple forces acting at once.
Methodology
Core idea
The calculator finds the inward net force or related circular-motion quantity needed for motion in a circle. In physics, that inward requirement is called centripetal force, and it comes from real forces such as tension, friction, normal force, gravity, or a combination [1].
Formulas used
a_c = v^2 / r
F_c = m * a_c
F_c = m * v^2 / r
a_c = omega^2 * r
F_c = m * omega^2 * r
v = omega * r
omega = 2 * pi / T
v = 2 * pi * r / T
g_force = a_c / g0
Here, a_c is centripetal acceleration, F_c is centripetal force, m is mass, v is speed, r is radius, omega is angular speed, T is period, and g0 = 9.80665 m/s^2 is standard gravity [2]. The acceleration and force relations are standard circular-motion results [1][3].
How each mode is solved
If Solve for is set to Centripetal force, the calculator uses mass, radius, and speed to find force, then also reports the matching centripetal acceleration and g value.
If it is set to Centripetal acceleration, it uses speed and radius first, then converts that acceleration into g units.
If it is set to Speed, it rearranges F_c = m * v^2 / r to get v = sqrt(F_c * r / m), then computes acceleration, angular speed, and period from that result.
If it is set to Angular speed, it rearranges F_c = m * omega^2 * r to get omega = sqrt(F_c / (m * r)), then computes speed and the other outputs.
If it is set to Period, it first finds speed from force, mass, and radius, then uses T = 2 * pi * r / v.
Worked mini-example
Suppose Mass (kg) is 2, Radius (m) is 5, and Speed (m/s) is 10.
a_c = 10^2 / 5 = 20 m/s^2
F_c = 2 * 20 = 40 N
g_force = 20 / 9.80665 = 2.039 g
So the object needs 40 N of inward net force, and its inward acceleration is about 2.039 g.
Display and validation rules
The calculator checks for impossible inputs before showing results. Radius must be greater than 0 in every mode, and any visible speed, angular speed, period, mass, or force input required by the selected mode must also be greater than 0. If not, it shows an error instead of NaN or Infinity.
Results are formatted in decimal, scientific, or auto mode. Auto is meant to keep everyday answers easy to read while still handling very large or very small values cleanly.
Assumptions behind the math
The formulas assume circular motion with a constant radius. They are most accurate for uniform circular motion, where the speed may stay constant even though the direction keeps changing [3]. Real objects can also have drag, changing speed, or uneven paths, so measured forces may differ from these ideal results.