Solve for α, a, or radius quickly. Use SI, imperial, or g units without confusion. Get results above the form, ready to share today.
Use these values to verify calculations quickly.
| Case | a (m/s²) | r (m) | α (rad/s²) | α (deg/s²) |
|---|---|---|---|---|
| Wheel edge | 2.50 | 0.35 | 7.1429 | 409.37 |
| Small pulley | 1.20 | 0.10 | 12.0000 | 687.55 |
| Drum rim | 0.80 | 0.50 | 1.6000 | 91.67 |
Tangential linear acceleration relates to angular acceleration by:
Where a is tangential acceleration, α is angular acceleration, and r is radius from the rotation axis.
This tool links tangential linear acceleration (a) to angular acceleration (α) at a chosen radius (r). It supports three modes: compute α from a and r, compute a from α and r, or compute r from a and α. Results are shown in both rad/s² and deg/s², plus common linear units.
For a point on a rotating body, tangential acceleration equals angular acceleration multiplied by radius. If a wheel edge is farther from the axis, the same α produces a larger a. Doubling r doubles a, while halving r doubles α for the same a.
Linear acceleration options include m/s², cm/s², mm/s², ft/s², in/s², and g. The calculator uses 1 g = 9.80665 m/s². Angular acceleration can be entered as rad/s² or deg/s², using 180° = π radians. Radius supports m, cm, mm, ft, and inches.
In small pulleys (r ≈ 0.05–0.15 m), α can exceed 50 rad/s² with modest a. Vehicle wheels (r ≈ 0.25–0.35 m) often see α in the 1–20 rad/s² range during normal starts. Robotics arms may use 0.10–0.60 m radii, depending on link length. Belt drives and turntables stay below 10 rad/s². In education labs, r is often 0.20–0.50 m for easy measurement.
If a = 2.50 m/s² and r = 0.35 m, then α = a/r = 7.1429 rad/s². Converting gives α ≈ 7.1429 × 57.2958 = 409.37 deg/s². This matches the example table and is useful for quick checks.
Use rad/s² when working with equations in SI form. Use deg/s² when comparing to motor controller readouts. If you solved for r, a negative radius indicates a sign mismatch; re-check your acceleration direction and sign convention.
Measure radius from the true rotation axis to the point of interest. Ensure you are using tangential acceleration, not centripetal acceleration (v²/r). Avoid r = 0 in α mode and α = 0 in r mode. Increase decimal places when values are small. If your radius has ±1 mm uncertainty, small radii can shift α noticeably. Record units alongside each value to prevent copy errors.
Yes. Convert first: r = diameter ÷ 2. Enter r in any supported length unit, then calculate. Using diameter directly will double or halve results incorrectly.
It is for tangential acceleration from changing speed. Centripetal acceleration depends on speed and radius (v²/r) and is not used in a = αr.
Select deg/s² in the angular unit menu. The calculator internally converts to rad/s² using π/180, then converts back for display and exports.
Negative results usually indicate a sign convention issue. Check your direction definitions for positive rotation and positive tangential direction. Magnitudes are often reported as positive when only size matters.
Yes, for a point on the rotating pulley or wheel. For rolling without slipping, tangential acceleration at the rim relates to linear acceleration of the contact point using the same a = αr relationship.
Run the calculation for each point of interest. Use the local distance from the rotation axis to that point. Larger r gives larger tangential acceleration for the same α.
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.