Use this right triangle calculator to solve missing sides, acute angles, area, and perimeter from any valid input pair.
Advanced options
How to use our Right Triangle Calculator
- Choose "What do you know?" to match the pair of values you already have.
- Enter the needed side length values in the visible side fields, keeping all side inputs in the same unit.
- If your mode uses an angle, choose "Reference angle" first so "opposite" and "adjacent" match the angle you mean.
- If your angle is in radians instead of degrees, open "Advanced options" and change "Angle unit" before entering "Acute angle (selected unit)".
- Enter one acute angle only. It must be more than 0 and less than 90 degrees, or more than 0 and less than pi/2 radians.
- Click "Calculate" to see the solved values for Leg a, Leg b, Hypotenuse c, Angle A, Angle B, Area, and Perimeter.
- Sanity-check the result: Hypotenuse c should be the longest side, Angle A plus Angle B should equal 90 degrees or pi/2 radians, and Area should be half of Leg a times Leg b.
Definitions
What do you know? The solve mode that tells the calculator which input pair you are using.
Leg a One of the two sides that meet at the right angle.
Leg b The other side that meets at the right angle.
Hypotenuse c The side opposite the 90 degree angle, and the longest side of a right triangle.
Reference angle The acute angle you choose as Angle A or Angle B so the words opposite and adjacent have a clear meaning.
Acute angle An angle smaller than 90 degrees, or smaller than pi/2 radians.
Opposite side The side directly across from the chosen reference angle.
Adjacent side The side next to the chosen reference angle, not counting the hypotenuse.
Area The amount of space inside the triangle. For a right triangle, it comes from the two legs.
Perimeter The total distance around the triangle, found by adding all three side lengths.
Common mistakes and quick fixes
Mistake: Choosing the wrong option in "What do you know?" and then typing values into fields that do not match your situation.
Fix: Pick the mode that matches your known pair first, then fill only the visible required inputs for that mode.
Mistake: Mixing up "Leg a (units)" and "Leg b (units)" when using "Reference angle" with an opposite or adjacent side mode.
Fix: Check "Reference angle" first. The opposite leg is across from that angle, and the adjacent leg is next to that angle, not counting "Hypotenuse c (units)".
Mistake: Entering a value in "Hypotenuse c (units)" that is equal to or smaller than a leg in one leg and hypotenuse mode.
Fix: Make sure "Hypotenuse c (units)" is longer than the known leg, because the hypotenuse is always the longest side.
Mistake: Typing radians into "Acute angle (selected unit)" while "Angle unit" is still set to degrees, or the other way around.
Fix: Set "Angle unit" first, then enter the angle. The outputs "Angle A" and "Angle B" will use that same unit.
Mistake: Using 0, a negative number, or an angle of 90 in "Acute angle (selected unit)".
Fix: Enter positive side lengths only, and keep "Acute angle (selected unit)" strictly between 0 and 90 degrees or between 0 and pi/2 radians.
Mistake: Reading "Area" or "Perimeter" without checking whether the solved triangle makes sense.
Fix: Confirm that "Hypotenuse c" is the longest side and that "Angle A" plus "Angle B" equals 90 degrees or pi/2 radians before using "Area" or "Perimeter".
Limitations & Key Assumptions / Boundary Conditions
- This calculator is only for right triangles, so it assumes one angle is exactly 90 degrees.
- You must enter a valid independent input pair for the selected mode. Extra hidden fields are ignored for the calculation.
- All side inputs must use the same length unit. The calculator does not convert inches, feet, meters, or other length units for you.
- The angle must be strictly between 0 and 90 degrees, or between 0 and pi/2 radians. Endpoints are not valid acute angles.
- In one leg and hypotenuse mode, the hypotenuse must be longer than the known leg or the triangle is impossible.
- Very tiny floating-point rounding effects can make values look slightly off from exact classroom numbers, especially for angles and trig-based cases.
- Area is reported in square units based on your side unit, but the unit name itself is not inferred or converted.
Methodology
How the calculator solves the triangle
The calculator uses the selected mode to decide which formula set applies. In every case, it solves the missing side lengths first, then the two acute angles, then Area and Perimeter.
c^2 = a^2 + b^2
c = sqrt(a^2 + b^2)
missing_leg = sqrt(c^2 - known_leg^2)
sin(theta) = opposite / hypotenuse
cos(theta) = adjacent / hypotenuse
tan(theta) = opposite / adjacent
other_acute = 90 deg - theta
other_acute = pi/2 - theta
Area = (a * b) / 2
P = a + b + c
Mode rules
If you know two legs, the calculator finds the hypotenuse with the Pythagorean theorem, then finds the acute angles from the side ratio. If you know one leg and the hypotenuse, it finds the other leg with sqrt(c^2 - known_leg^2). If you know one side and one acute angle, it uses sine, cosine, or tangent based on whether the known side is opposite, adjacent, or the hypotenuse [2][4].
The reference angle matters in side-angle modes. When you choose Angle A, the side opposite Angle A is treated as the opposite leg for that angle, and the other leg is adjacent. When you choose Angle B, those roles switch.
Mini example
Suppose you choose "Two legs" and enter Leg a = 3 and Leg b = 4.
c = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5
Area = (3 * 4) / 2 = 6
P = 3 + 4 + 5 = 12
Then the acute angles are found from trig ratios, giving about 36.87 degrees and 53.13 degrees. They add to 90 degrees, which is a good check for a right triangle.
Angle units
If "Angle unit" is set to degrees, outputs stay in degrees. If it is set to radians, the calculator uses pi/2 for the right angle complement and reports both acute angles in radians. Degree-radian conversion uses pi/180 and 180/pi.
Error handling and assumptions
The calculator blocks non-numeric, zero, and negative side lengths. It also blocks acute angles outside the valid range and rejects impossible leg-hypotenuse pairs where the hypotenuse is not longer than the leg. Hidden inputs are ignored so old values from another mode do not affect the current result.
This method assumes an exact right triangle and standard right-triangle trigonometry. Real measured triangles can differ a little because of rounding or measurement error.