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Involute Function Calculator.

Evaluate a circle involute at radius a and parameter t (radians).

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Set your values

Results update as you type.

x: 2.763547 units

x

0.000000units
y: 0.602337 units

y

0.000000units
Distance: 2.828427 units

Distance

0.000000units

Results update automatically as you type.

Use Cases

Designing gear tooth profiles

Involute curves are fundamental in gear design. This calculator helps engineers quickly find coordinates for involute gear tooth profiles, aiding in CAD modeling and manufacturing.

Example: Calculate points for a gear with base radius 10 mm at t = 0.5 rad.

Educational visualization

Students and educators can use this tool to explore the mathematical properties of involutes, understanding how the curve changes with radius and parameter t.

Example: Plot multiple points by varying t from 0 to 2π.

Frequently Asked Questions

What is the involute of a circle?
The involute of a circle is a curve traced by the end of a taut string unwinding from a circle. It is defined parametrically using the base-circle radius and a parameter t, which represents the angle of unwinding in radians.
How do I use this calculator?
Enter the base-circle radius (in any unit) and the parameter t (in radians). The calculator will compute the x and y coordinates of the point on the involute curve using the standard parametric equations.
What units should I use for the radius?
You can use any unit (e.g., meters, inches, pixels) as long as you are consistent. The output coordinates will be in the same unit as the radius input.

Tips & Common Mistakes

Tips

  • Ensure the parameter t is in radians, not degrees, for correct results.
  • Use consistent units for the radius and interpret the output coordinates in the same units.
  • For a complete curve, evaluate multiple t values (e.g., 0 to 2π) and plot the points.
  • Remember that t represents the unwinding angle; larger t values produce points further from the base circle.

Common Mistakes to Avoid

  • Entering the diameter instead of the radius. The calculator expects the base-circle radius.
  • Using degrees for t without converting to radians. Multiply degrees by π/180.
  • Confusing the parameter t with time; it is an angle parameter, not a time variable.

Last updated: August 13, 2026