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Math • 45 45 90 Triangle Calculator

45 45 90 Triangle Calculator

Calculate the hypotenuse, area, and side relationships of a 45-45-90 special right triangle.

Hypotenuse (c)
5.000
√(a² + b²)
Angle ∠A
36.87°
arctan(a / b)
Angle ∠B
53.13°
90° - ∠A
Triangle Area
6.00
½ × a × b
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Calculation Guide & Reference

45-45-90 Special Right Triangle Mathematics

45-45-90 triangle calculator computes the hypotenuse, legs, and area of this special right triangle where both legs are equal.

Standardized Mathematical Formula
Hypotenuse = Leg × √2

A 45-45-90 triangle is an isosceles right triangle — both legs are equal length, and the hypotenuse is always the leg length multiplied by √2 (≈1.41421).

Variables:
Leg:Either of the two equal legs
Hypotenuse:The longest side, opposite the right angle
How It Works (Step-by-Step)
  • 1Enter the same value for both legs (a 45-45-90 triangle always has equal legs).
  • 2View the hypotenuse, area, and confirm both non-right angles are exactly 45°.
Real-World Numerical Example
A 45-45-90 Triangle with Legs of 5

A right triangle has two equal legs of length 5, making it a 45-45-90 triangle.

•Hypotenuse: 5 × √2 ≈ 7.07.
•Area: (1/2) × 5 × 5 = 12.5 square units.
•Both non-right angles: 45° each.
Result: The triangle has a hypotenuse of about 7.07, an area of 12.5 square units, and two 45° angles.
Calculation Best Practices & Tips
Examine the discriminant (b² - 4ac) before solving quadratics to instantly know if roots are real, distinct, repeated, or complex.
In statistical analysis, always check both the mean and median to identify if data distribution is skewed by outliers.
When calculating percentage changes, ensure you divide by the original starting baseline value: ((New - Old) / Old) * 100.

Frequently Asked Questions (FAQ)

The side ratio is 1 : 1 : √2 — both legs are equal, and the hypotenuse is √2 times longer than either leg.

A 45-45-90 triangle is isosceles (two equal legs, two 45° angles), while a 30-60-90 triangle has three different side lengths and angles — both are common "special" right triangles with fixed side ratios, but the ratios differ (1:1:√2 vs 1:√3:2).

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