Last updated: July 31, 2026
Isosceles Right Triangle Hypotenuse Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
From leg: hypotenuse = leg√2. From hypotenuse: leg = hypotenuse/√2.
Where:
- a=Equal leg length
- c=Hypotenuse
Worked Examples
From a leg of 5
Start with the equal leg and compute the hypotenuse.
- 1Use c = a√2.
- 2Multiply 5 by √2.
- 3Return the original leg alongside the computed hypotenuse.
From a hypotenuse of 10
Work backward from the long side to the equal leg.
- 1Use a = c/√2.
- 2Divide 10 by √2.
- 3Echo the original hypotenuse and report the computed leg.
Decimal leg input
A leg of 8.25 still uses the same √2 scaling.
- 1Multiply 8.25 by √2.
- 2Round the result to 6 decimals.
- 3Review both displayed side lengths.
Invalid mode example
An unsupported mode returns safe defaults.
- 1Check the mode string first.
- 2Reject anything other than fromLeg or fromHypotenuse.
- 3Return zeros with an error message.
Introduction
This calculator handles the most common 45-45-90 side conversion in both directions. Choose whether you know a leg or the hypotenuse, then the tool fills in the missing side using the fixed square-root-of-two relationship.
Two-Way Side Conversion
Unlike a one-direction calculator, this tool can start from either of the two distinct side types in an isosceles right triangle.
From leg to hypotenuse
From hypotenuse to leg
Echoes the provided side for clarity
Mode: From Leg
When a leg is known, the missing hypotenuse is just that leg multiplied by √2.
- Formula:
c = a√2
- Input requirement:
leg > 0
Output returns both leg and hypotenuse
Mode: From Hypotenuse
When the hypotenuse is known, divide by √2 to recover the equal leg length.
- Formula:
a = c/√2
- Input requirement:
hypotenuse > 0
Useful for reversing a diagonal measurement
How to Choose the Correct Mode
Pick the mode that matches the side you already know. The unused numeric input is ignored.
Use From Leg for equal side lengths
Use From Hypotenuse for the longest side
Switching modes changes which input is validated
Validation Rules
Only the active input must be positive and finite. Invalid modes and non-positive values return zeros and an error string.
Leg must be positive in From Leg mode
Hypotenuse must be positive in From Hypotenuse mode
Mode must match one of the two supported options
Practical Uses
This kind of conversion shows up whenever square corners create a diagonal, such as tiles, screens, framing, and coordinate geometry.
Square diagonal checks
Blueprint and layout calculations
Geometry practice
Fast reverse calculations from measured diagonals
Rounding and Interpretation
Results are rounded to 6 decimals for clean display while preserving enough precision for most educational and practical needs.
Exact values involve √2
Rounded outputs are easier to read
Echoed inputs help prevent confusion about which side was provided
FAQs
What does the mode field do?
It tells the calculator whether to compute from a leg or from the hypotenuse.
Why does the calculator return both side values?
Showing both the given and computed side makes it easier to confirm the conversion direction.
What formula is used from a leg?
It uses c = a√2, the standard 45-45-90 triangle relationship.
What formula is used from a hypotenuse?
It uses a = c/√2, which is the inverse of the hypotenuse formula.
Can I leave the unused input blank?
Yes. Only the input required by the selected mode is validated.
What if I enter a negative value?
The calculator returns zeroed outputs and an error because side lengths must be positive.
Is this different from the full isosceles right triangle calculator?
Yes. This one focuses only on the side conversion, while the full calculator also returns area, perimeter, and angles.