Skip to main content
Calcimator

Angle Calculator

Convert angles between degrees, radians, and gradians. Find complementary and supplementary angles, plus sine, cosine, and tangent values.

About this calculator

This calculator takes one angle in degrees and derives every other common way of describing it: radians (multiply by pi over 180), gradians (multiply by 10 over 9, since a full turn is 400 gradians instead of 360 degrees), the complementary angle (90 degrees minus the input), the supplementary angle (180 degrees minus the input), and the three primary trig ratios evaluated at that angle. Sine and cosine move in opposite directions across the 0 to 90 degree range the default value sits inside — as the angle rises, sine climbs toward 1 while cosine falls toward 0 — which is a genuine, checkable property of the two functions rather than a coincidence of this particular page. Tangent gets special handling: at 90 degrees and 270 degrees, and any angle 180 degrees apart from those, the geometric ratio is undefined because cosine sits at exactly zero in the denominator, so the calculator reports the word undefined instead of an enormous or infinite number that would be misleading to read as data.

The input itself is not restricted to a clean multiple of anything — entering 45.3 degrees works exactly like entering 45, because nothing in the underlying formulas rounds the angle before using it; the whole-number stepper on the field is a convenience for dragging the slider, not a constraint the calculation enforces. Angles outside minus 360 to 360 degrees fall outside the field's configured range and are not exercised here.

Inputs

°

Results

Degrees

45°

Radians0.785398
Gradians50
Complementary (90° - θ)45°
Supplementary (180° - θ)135°
sin(θ)0.707107
cos(θ)0.707107
tan(θ)1
How to Use This Calculator
  1. Enter an angle in degrees (from -360 to 360) in the Angle field; the calculator converts it to radians (rad = deg × π/180) and gradians (grad = deg × 10/9).
  2. Complementary angle = 90° − θ; Supplementary angle = 180° − θ, both always shown alongside the conversions.
  3. sin(θ), cos(θ), and tan(θ) are computed at the entered angle.
  4. Tan is undefined at angles like 90° and 270°; the calculator flags these cases rather than showing a numeric value.
  5. Use the Slope Calculator to convert a rise/run ratio into the equivalent angle of inclination.

How the result changes with Angle

AngleDegrees
2323°
3434°
6868°
113113°

What each input means

Angle
Angle in degrees.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    Angle = 45 = 1 input(s) provided
  2. Calculate Degrees
    Degrees = angle
    45 = 45
  3. Calculate Radians
    Radians
    0.785398 = 0.785398
  4. Calculate Gradians
    Gradians
    50 = 50

Engine last updated . Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

Why do sine and cosine move in opposite directions here?

Across the 0 to 90 degree range this calculator's default sits inside, sine rises as the angle increases while cosine falls — raising the angle from 40.5 to 49.5 degrees pushes sine up and cosine down by roughly the same amount. That is a property of the two functions themselves, not something specific to this tool.

Why does tangent show undefined instead of a number at 90 degrees?

Tangent is sine divided by cosine, and cosine reaches exactly zero at 90 degrees and 270 degrees. Dividing by zero has no finite answer, so rather than display an enormous or infinite value that would look like real data, the calculator reports the word undefined at those points.

Can I enter an angle with a decimal, like 33.5 degrees?

Yes. Nothing in the underlying formulas rounds the angle before using it, so a decimal value flows through the radian conversion and trig functions exactly like a whole number would. The stepper on the input field only controls how the slider moves, not what the field will accept.

What is a gradian, and why is the conversion factor 10/9?

A gradian divides a full circle into 400 equal parts instead of the 360 degrees most people are used to, a system that surveying and some European engineering fields still use. Since 400 gradians equal 360 degrees, one degree equals 400 divided by 360, which simplifies to 10 over 9 gradians.

The questions that sit next to this one — chosen by subject, including calculators filed under a different category.

More in Math & Statistics.