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Complementary and Supplementary Angle Calculator
Type an angle in degrees, radians, gradians or degrees-minutes-seconds to get its complement (adds to 90°), supplement (adds to 180°) and explement (adds to 360°). Each answer is shown in every unit, with the subtraction worked out and a diagram of each angle pair.
How to use the Complementary and Supplementary Angle Calculator
Enter the angle as a decimal, in DMS like 28°15'40", or as a multiple of pi.
Pick the unit: degrees, radians or gradians.
Read the complement and supplement at the top, and the explement below.
Look at the diagrams to see how each pair fills a right angle, a straight line or a full turn.
Use the table for the same answers in radians, π radians, DMS and gradians.
Angle pair formulas
Pair
Angles add up to
Formula (degrees)
Formula (radians)
Exists when
Complementary
90° (right angle)
90° − θ
π/2 − θ
0° < θ < 90°
Supplementary
180° (straight line)
180° − θ
π − θ
0° < θ < 180°
Explementary (conjugate)
360° (full turn)
360° − θ
2π − θ
0° < θ < 360°
Common angles and their pairs
Angle
Radians
Complement
Supplement
Explement
15°
π/12
75°
165°
345°
30°
π/6
60°
150°
330°
36°
π/5
54°
144°
324°
45°
π/4
45°
135°
315°
60°
π/3
30°
120°
300°
72°
2π/5
18°
108°
288°
90°
π/2
none (0°)
90°
270°
120°
2π/3
none
60°
240°
150°
5π/6
none
30°
210°
Where angle pairs show up
Right triangles: the two acute angles are complementary, so knowing one gives the other. That is why sin θ = cos(90° − θ): the "co" in cosine stands for complement.
Straight lines: angles that form a linear pair, like the two angles on either side of a line crossing another, are supplementary.
Parallel lines: co-interior (same-side interior) angles between two parallel lines are supplementary, which is a quick check in geometry proofs.
Cyclic quadrilaterals: opposite angles of a quadrilateral inscribed in a circle are supplementary.
Trigonometry: sin(180° − θ) = sin θ and cos(180° − θ) = −cos θ, so supplements share a sine.
To work with DMS answers, remember that 1° = 60′ (minutes) and 1′ = 60″ (seconds). For example, 90° − 28°15′40″ is easiest as 89°59′60″ − 28°15′40″ = 61°44′20″.
Frequently asked questions
What are complementary angles?
Two angles are complementary when they add up to 90°, a right angle. The complement of θ is 90° − θ, so the complement of 35° is 55°. In radians the complement is π/2 − θ.
What are supplementary angles?
Two angles are supplementary when they add up to 180°, a straight line. The supplement of θ is 180° − θ, so the supplement of 35° is 145°. In radians the supplement is π − θ.
How can I remember which is which?
A common memory aid: C comes before S in the alphabet, just as 90 comes before 180. Another one is that complementary has a corner (90°) and supplementary is straight (180°).
Does an obtuse angle have a complement?
No. A complement must be a positive angle, and 90° − θ is negative or zero whenever θ is 90° or more. So only acute angles have complements. Angles from 90° up to (but not including) 180° still have supplements.
What is an explementary angle?
Explementary angles, also called conjugate angles, add up to 360°, a full turn. The explement of θ is 360° − θ, so the explement of 250° is 110°. Any angle between 0° and 360° has one.
Do complementary angles have to be next to each other?
No. Any two angles whose measures sum to 90° are complementary, whether or not they share a side. When they are adjacent they form a right angle; for example, the two acute angles of a right triangle are always complementary.
How do I find the complement of an angle in radians?
Subtract it from π/2 ≈ 1.5708. For θ = π/6, the complement is π/2 − π/6 = π/3 ≈ 1.0472 rad. For the supplement subtract from π ≈ 3.1416 instead.
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