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Quickly calculate the centripetal force required for uniform circular motion by entering mass, velocity, and radius.
Enter mass, radius, and a known quantity to see the centripetal force.
Overview
Understand what the tool solves, how it works, and the boundaries of its data.
Enter an object's mass and the radius of its circular path, then provide one known motion quantity: linear velocity, angular velocity, or the time for one revolution (period). The result includes centripetal force in newtons (N), centripetal acceleration in meters per second squared (m/s²), and the corresponding linear velocity, angular velocity, and period. Calculation steps show how the selected input leads to the result.
Centripetal means directed toward the center. In circular motion, the direction of velocity changes, so the object accelerates inward even when its speed stays constant. The required centripetal force is the inward component of the net force; it is not an extra force that must always come from a particular source. Depending on the situation, tension, gravity, friction, a track's normal force, or a combination can provide it.
ac = v² / r = ω²r
Fc = mac = mv² / r = mω²r
v = ωr; ω = 2π / T
Here, m is mass, r is radius, v is linear speed, ω is angular speed, and T is the period. A larger speed has a squared effect: doubling speed with mass and radius unchanged makes the required force four times as large. At fixed mass and speed, doubling the radius halves the force. These comparisons hold only when the other stated quantities stay fixed.
Guide
Follow the workflow and verify inputs and outputs with practical examples.
Enter mass in kilograms (kg) and the path radius in meters (m). Use the radius from the center of the circular path to the object's path; if a problem gives diameter, divide it by two first.
Use linear velocity in meters per second (m/s), angular velocity in radians per second (rad/s), or period in seconds (s), according to the value you have. The input fields accept numbers and do not convert units automatically.
The force and acceleration appear with the calculated linear velocity, angular velocity, and period. Review the displayed solution steps to check the substitution. For example, with m = 2 kg, r = 0.5 m, and v = 3 m/s: ac = 3² / 0.5 = 18 m/s², and Fc = 2 × 18 = 36 N. The derived angular speed is 6 rad/s and period is about 1.0472 s.
Use cases
See how the tool fits into real work and everyday tasks.
When a physics problem gives mass, radius, and speed, enter those SI values and compare both the force and acceleration with your hand calculation. The steps help identify a squared-speed or radius substitution error.
If you know how long one revolution takes but not the tangential speed, choose period mode. The calculator derives angular and linear speed before finding acceleration and force, so you can compare the intermediate values with a lab record.
Keep mass and radius fixed while changing speed, or keep mass and speed fixed while changing radius. Comparing the outputs makes the square dependence on speed and inverse dependence on radius visible.
Q&A
Find concise answers to common questions and confusing cases.
Convert values before entering them. Use kg, m, m/s, rad/s, or seconds for the selected fields. For example, convert rotational rate to radians per second or find the period in seconds; this calculator does not provide a unit-conversion mode.
A zero linear or angular speed gives zero centripetal acceleration and force, but T = 2π/ω has no finite period when ω is zero. The calculator therefore leaves the period blank in that case.
Not necessarily. It is the magnitude of the net inward force required for the stated circular motion. To identify an individual force such as tension or friction, analyze the forces in the specific setup.
Mass and radius must be positive. Linear velocity and angular velocity may be zero or positive, while period must be positive. Check that the selected mode has a number entered and that all values use the required units.
Notes
Review scope, result limitations, and important precautions before use.
These relationships describe the radial, inward acceleration and net-force magnitude for an ideal circular path. If speed changes, there can also be tangential acceleration; this calculation does not find that component, identify the forces in a particular system, or determine whether a road, ride, or device is safe.
The result depends on the values and units entered and is displayed with compact numeric formatting. Measurement uncertainty in mass, radius, speed, or timing carries through to the calculated result. Use a complete force analysis and appropriate professional review for real equipment, transportation, or safety decisions.
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