Math
Complementary and Supplementary Angles Calculator
Two angles are complementary when they add to 90°, supplementary when they add to 180°, and explementary (conjugate) when they add to 360°.
Enter one angle and get all three partners in degrees and radians, plus a note whenever a partner does not exist, such as the complement of 120°.
Type a number, a fraction, a π expression like π/3, or degrees-minutes-seconds like 35° 20′.
Try an example
Result
Complementary angle (adds to 90°)
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- Supplementary angle (adds to 180°)
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- Explementary angle (adds to 360°)
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- Angle type
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- Degrees-minutes-seconds
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Study path
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Definitions and formulas
Where you see them
- The two acute angles of a right triangle are complementary, which is why sin θ = cos(90° − θ).
- Angles on a straight line (a linear pair) are supplementary.
- Consecutive interior angles between parallel lines are supplementary.
- An angle and its reflex partner around a point are explementary.
How to use it
- Enter the angle in degrees, An angle unit where a full turn is 2π instead of 360 degrees., gradians, or turns.
- Read the complement, supplement, and explement. Each shows degrees and the radian form.
- If a partner reads none, the angle is too large for that pair; the steps still show the subtraction so you can see why.
How to read the answer
- Complement and angle are both acute; supplement of an acute angle is obtuse; supplement of an obtuse angle is acute.
- A 90° angle has no complement (the partner would be 0°) and its supplement is 90°.
- The angle type line names the original angle: acute, right, obtuse, straight, or reflex.
Common mistakes and edge cases
- Subtracting from the wrong total: complementary uses 90°, supplementary uses 180°.
- Reporting a negative complement: 90° − 120° = -30° is not an angle, so 120° has no complement.
- Mixing radians and degrees: the complement of π/3 is π/2 − π/3 = π/6, not 90 − π/3.
- Assuming complementary angles must be adjacent: they only need to add to 90°.
Worked examples
Acute angle
35°
Complementary angle (adds to 90°)
55° (11π/36)
Radians
π/3
Complementary angle (adds to 90°)
π/6 (30°)
Obtuse angle
120° has no complement
Complementary angle (adds to 90°)
none (angle must be strictly between 0° and the total)
Right angle
90° has no complement
Complementary angle (adds to 90°)
none (angle must be strictly between 0° and the total)
Degrees-minutes-seconds
35° 20′ 15″
Complementary angle (adds to 90°)
54.6625° (0.954 rad)
Reflex angle
200° only has an explement
Complementary angle (adds to 90°)
none (angle must be strictly between 0° and the total)
Unreadable input
Complementary angle (adds to 90°)
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Frequently asked questions
What is the complement of 35 degrees?+
55°, because 90° − 35° = 55°. Its supplement is 145° and its explement is 325°.
Can an obtuse angle have a complement?+
No. Complementary angles add to 90°, so both must be acute. An obtuse angle such as 120° has a supplement (60°) but no complement.
What is an explementary angle?+
Also called a conjugate angle: the partner that completes a full 360° turn. The explement of 100° is 260°.
Do complementary angles have to be next to each other?+
No. Adjacency is not required; the only condition is that the measures add to 90°.
How do complementary angles work in radians?+
Subtract from π/2 instead of 90°. The complement of π/6 is π/2 − π/6 = π/3. Supplementary angles subtract from π.
Why does sin 35° equal cos 55°?+
Because 35° and 55° are complementary. In a right triangle the side opposite one acute angle is adjacent to the other, so sine of one equals cosine of the other.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026