About the Complementary and Supplementary Angles Calculator
This calculator finds the missing angle in the three classic angle pairs. The complement of an angle is what you add to reach 90° (a right angle), the supplement is what you add to reach 180° (a straight line), and the explement (or conjugate) is what you add to reach 360° (a full turn). Enter your angle in degrees or radians and all three are shown, along with the angle’s type — acute, right, obtuse, straight or reflex.
It is useful for geometry homework on parallel lines and transversals, linear pairs and triangle angle sums, and for practical jobs such as cutting mitre and bevel angles in carpentry, where the saw setting is often the complement of the angle you need.
Only positive complements and supplements are shown: an angle of 90° or more has no complement, and an angle of 180° or more has no supplement, so those results display a dash.
With the default inputs, the supplementary angle (to 180° / π) is 145. Change any value above to recalculate instantly.
How to use the complementary and supplementary angles calculator
- 1Enter the angle you know.
- 2Choose degrees or radians.
- 3Read the supplementary, complementary and explementary angles.
- 4Check the angle type and the value converted to the other unit.
Formula and method
Two angles are complementary when they add up to 90°, supplementary when they add up to 180° and explementary (conjugate) when they add up to 360°. So each missing angle is simply the target total minus your angle. In radians the targets are π/2, π and 2π.
Complements and supplements are defined only for positive results, so an angle of 90° or more has no complement and an angle of 180° or more has no supplement. The angle type follows the usual definitions: acute below 90°, right at 90°, obtuse between 90° and 180°, straight at 180° and reflex between 180° and 360°.
- θ
- The given angle
- π
- ≈ 3.14159; 180° equals π radians
Worked examples
Angle of 35°
The supplement is 180° − 35° = 145°, the complement is 90° − 35° = 55° and the explement is 360° − 35° = 325°. 35° is acute and equals about 0.6109 radians.
Obtuse angle of 120°
A 120° angle has a supplement of 60° and an explement of 240°, but no complement, because it is already larger than a right angle.
Angle of 1.2 radians
In radians the supplement is π − 1.2 ≈ 1.9416 and the complement is π/2 − 1.2 ≈ 0.3708. The angle itself is about 68.75°.
Frequently asked questions
What is a supplementary angle?+
Two angles are supplementary if they add up to 180°. The supplement of an angle θ is 180° − θ, so the supplement of 35° is 145°. Adjacent supplementary angles form a straight line.
What is a complementary angle?+
Two angles are complementary if they add up to 90°. The complement of θ is 90° − θ, so the complement of 35° is 55°. The two acute angles of any right triangle are complementary.
What is an explementary angle?+
Explementary (or conjugate) angles add up to 360°, a full turn. The explement of 120° is 240°; together they go all the way around a point.
Can an obtuse angle have a complement?+
No. An obtuse angle is already more than 90°, so no positive angle can be added to make 90°. It still has a supplement as long as it is less than 180°.
How do I remember complementary vs supplementary?+
A common trick: “C” comes before “S” in the alphabet just as 90 comes before 180. Or think “complementary makes a Corner (90°), supplementary makes a Straight line (180°)”.