Angle Calculator
Right Triangle Missing Angle Calculator
Enter one acute angle and instantly find the other - the two acute angles in every right triangle always add up to 90°.
Calculate Missing Angle
This calculator finds Angle B using .
Enter inputs to calculate Angle B.
Angle B
Result-
Solution Steps
Formula:
What This Tool Does
Every right triangle has one fixed 90° angle, so the two remaining acute angles must share exactly 90°. This calculator subtracts the angle you know from 90° to reveal the one you don't.
No side lengths are needed - just type in the known acute angle (between 0° and 90°) and the complementary angle appears instantly.
Known values
One acute angle (A or B)
Finds
The other acute angle in degrees
Formula
B = 90° − A
Validation
Input must be between 0° and 90° (exclusive)
Complementary Angle Formulas
A right triangle’s three angles total 180°. One is fixed at 90°, so the remaining two acute angles share 90°. Knowing either one instantly gives the other.
A + B = 90°
A = 90° − B
Triangle Diagram
Angle A and Angle B are the two acute angles. Together, they add up to the 90° angle at corner C, which means A + B = 90°.
Highlighted relationship
A + B = 90°
In every right triangle, the two acute angles always add up to 90° because the third angle is already 90°.
Diagram Key
- a = opposite side The side across from angle A.
- b = adjacent side The side next to angle A.
- c = hypotenuse The longest side, opposite the right angle.
- A = reference angle The acute angle used by sine, cosine, and tangent on these pages.
- B = other acute angle The complementary acute angle in the same right triangle.
Quick Checks
- The 90° angle is at corner C.
- Both acute angles must be less than 90°.
How to Use This Calculator
- Enter the acute angle you already know (must be between 0° and 90°).
- Press Calculate.
- Read the complementary acute angle from the result.
- Verify by adding both angles - they must equal exactly 90°.
Step-by-Step Example
Let's assume you know that angle A is exactly 36.87°.
The missing angle B is 53.13 degrees.
What the Result Means
The output is the other acute angle in the same right triangle. A small input produces a large complement, and vice versa.
Both acute angles together always account for the 90° that the right angle leaves over. Neither one can equal 0° or 90°.
When to Use This Calculator
Use this calculator as the final step after finding one angle through sine, cosine, or tangent.
- Completing a triangle diagram for homework, drafting, or CAD layouts.
- Checking that your trig-calculated angle and its complement add to 90°.
- Finding the second angle for construction cuts where both miter angles matter.
Common Mistakes
Avoid these common mistakes:
- Subtracting from 180° instead of 90°.
- Entering the 90° angle.
- Using an angle bigger than 90°.
- Forgetting that only the two acute angles add to 90°.
Frequently Asked Questions
Answers to the most common right-triangle solving questions.
01 What does the formula B = 90° - A actually do? expand_more
This simple subtraction formula takes the total available 90 degrees shared by the acute corners and removes the angle you already know, leaving exactly what is left for the missing corner.
02 What does the final missing angle result mean? expand_more
It represents the exact degree measurement of the final empty corner in your right triangle. Finding this number completes the triangle so all three corners add perfectly to 180 degrees.
03 Why do the two angles always add up to 90 degrees? expand_more
Every triangle holds exactly 180 degrees. Since a right triangle always has one 90-degree corner, that leaves exactly 90 degrees left over to be shared between the remaining two corners.
04 Can one of the acute angles be exactly 90 degrees? expand_more
No. If one of them was 90 degrees, the other would have to be 0 degrees, which means the triangle would flatten into a single straight line.
05 Do I need to know the lengths of the sides to find the missing angle? expand_more
Not at all. As long as you know one of the acute angles, the sides don't matter for this specific calculation.