Calculate adjusted angles, angle differences, unit conversions, and right triangle sides, area, and acute angles from known values.
Angle Adjustment Formulas
The calculator runs a different formula depending on which tab you choose.
Adjust angle. Add or subtract one angle from another, then wrap the result into the 0° to 360° range.
final = (start ± change) mod 360
Angle between two directions. Take the difference and normalize it both ways around the circle.
clockwise = (B - A) mod 360 counterclockwise = (A - B) mod 360 shortest = min(clockwise, counterclockwise)
Unit conversion. All units route through degrees.
deg = rad * 180/pi = grad * 0.9 = turn * 360
Right triangle. Solve the triangle, then read the acute angles.
c = sqrt(a^2 + b^2) area = a * b / 2 alpha = arcsin(a / c) beta = 90° - alpha
- start: the angle you begin with
- change: the amount you add or subtract
- A, B: two angles or line directions measured from the same reference
- rad, grad, turn: angle in radians, gradians, or full turns
- a, b: legs of a right triangle
- c: hypotenuse
- alpha, beta: the two acute angles, opposite legs a and b
Assumptions: angles are signed, with positive values rotating counterclockwise. Results are normalized to a single turn (0° to 360°), but the unwrapped value is also shown so you can see the raw sum. Right triangle inputs must be positive, and any leg must be shorter than the hypotenuse you provide.
Each tab maps to one job. Use Adjust angle when you need a heading after turning. Use Angle between when you have two bearings and want the gap. Use Convert to move a single value across degree, radian, gradian, or turn units. Use Right triangle when you know two sides or one side and the area and want the angles.
Reference Tables
Common angles in every unit the calculator supports:
| Degrees | Radians | Gradians | Turns |
|---|---|---|---|
| 0° | 0 | 0 | 0 |
| 30° | π/6 ≈ 0.5236 | 33.33 | 1/12 |
| 45° | π/4 ≈ 0.7854 | 50 | 1/8 |
| 60° | π/3 ≈ 1.0472 | 66.67 | 1/6 |
| 90° | π/2 ≈ 1.5708 | 100 | 1/4 |
| 180° | π ≈ 3.1416 | 200 | 1/2 |
| 270° | 3π/2 ≈ 4.7124 | 300 | 3/4 |
| 360° | 2π ≈ 6.2832 | 400 | 1 |
Quadrant guide for the wrapped result:
| Range | Quadrant | Sin / Cos signs |
|---|---|---|
| 0° to 90° | I | + / + |
| 90° to 180° | II | + / − |
| 180° to 270° | III | − / − |
| 270° to 360° | IV | − / + |
Worked Examples
Example 1: Wrap past 360°. Start at 350° and add 25°. The raw sum is 375°. Subtract 360° to wrap: the final angle is 15°.
Example 2: Subtract through zero. Start at 20° and subtract 50°. The raw sum is −30°. Add 360°: the final angle is 330°.
Example 3: Angle between bearings. Line A points at 15°, line B at 110°. Going clockwise from A to B is 95°. Going counterclockwise is 265°. The shortest separation is 95°.
Example 4: Right triangle from two legs. With a = 3 and b = 4, the hypotenuse is 5. The angle opposite a is arcsin(3/5) = 36.87°, and the other acute angle is 53.13°.
FAQ
Why is my result different from the unwrapped sum? The main result is normalized to one full turn. The unwrapped value shows the raw sum before wrapping, which can exceed 360° or be negative.
Does the calculator handle negative angles? Yes. Enter any signed value. Negative inputs rotate clockwise from the reference direction.
What is a gradian? A gradian splits a right angle into 100 parts, so a full turn is 400 gradians. It is used in some surveying and engineering contexts.
Which acute angle is alpha in the right triangle mode? Alpha is opposite leg a, and beta is opposite leg b. They always add to 90°.
Can I use the angle-between mode for compass bearings? Yes, as long as both bearings are measured from the same reference and in the same rotation direction. The clockwise and counterclockwise outputs cover both interpretations.