Pythagorean Theorem Calculator to Find Missing Length of Right Triangle

Pythagorean Theorem Calculator Sign

This calculator will use the Pythagorean Theorem to solve for the missing length of a right triangle given the lengths of the other two sides.

Plus, unlike other online calculators, this calculator will show its work and draw the shape of the right triangle based on the results.

Finally, the Learn tab also includes a mini calculator that checks to see if the given lengths of three sides of a triangle form a right triangle (Converse of Pythagorean Theorem).

If you are unfamiliar with the Pythagorean Theorem, it may help to visit the Learn tab before using the calculator.

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Pythagorean Theorem Calculator

Find the hypotenuse of a right triangle, or the length of any missing side, using the Pythagorean Theorem.

Learn More

Selected Data Record:

A Data Record is a set of calculator entries that are stored in your web browser's Local Storage. If a Data Record is currently selected in the "Data" tab, this line will list the name you gave to that data record. If no data record is selected, or you have no entries stored for this calculator, the line will display "None".

DataData recordData recordSelected data record: None
Dec places:Decimal places:Number of decimal places:Number of decimal places to round result to:

Number of decimal places:

Select how many decimal places you would like the result rounded to. Note that you can change the number of places before or after calculating the missing length. Also note that the Pythagorean Theorem Calculator will always display the raw results (out to 14 places) in the steps that will appear beneath the calculator.

Solve for:

Solve for:

Select the right triangle side you wish to solve for.

Length ofLength of Leg a:

Length of 1st Known Length:

Enter the length associated to the label on this line.

#
Length ofLength of Leg b:

Length of 2nd Known Leg:

Enter the length associated to the label on this line.

#
Length ofLength ofHypotenuse:

Length of missing side:

This is the missing length of the right triangle.

AreaAreaArea of triangleArea of triangle:

Area of triangle:

This is the area of the right triangle formed by Leg a, Leg b, and Leg c (hypotenuse). The formula used is, Area (K) = 1/2 x b x a.

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If you would like to save the current entries to the secure online database, tap or click on the Data tab, select "New Data Record", give the data record a name, then tap or click the Save button. To save changes to previously saved entries, simply tap the Save button. Please select and "Clear" any data records you no longer need.

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Help and Tools

Learn

What the Pythagorean Theorem is and how it is used.

What is the Pythagorean Theorem?

The Pythagorean Theorem is the relationship between the lengths of the two legs of a right triangle and its hypotenuse. The relationship is expressed as follows:

a2 + b2 = c2
where ...
a = the length of the vertical side.
b = the length of the base.
c = the length of the side opposite of the 90° angle.

Based on this relationship, we can isolate each unknown length to solve for it.

Hypotenuse c =a2 + b2
Leg a =c2 - b2
Leg b =c2 - a2
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Converse of Pythagorean Theorem

If you already know the lengths of all three sides of a triangle, the Converse of the Pythagorean Theorem can be used to determine whether or not the triangle is a right triangle.

If a2 + b2 = c2 is true, then the triangle is a right triangle.
If a2 + b2 = c2 is false, then the triangle is not a right triangle.

You can conduct your own test here:

Converse Test Calculator
a b c
222
+=
+=
=
Enter values for a, b, and c

Adjust Calculator Width:

Move the slider to left and right to adjust the calculator width. Note that the Help and Tools panel will be hidden when the calculator is too wide to fit both on the screen. Moving the slider to the left will bring the instructions and tools panel back into view.

Also note that some calculators will reformat to accommodate the screen size as you make the calculator wider or narrower. If the calculator is narrow, columns of entry rows will be converted to a vertical entry form, whereas a wider calculator will display columns of entry rows, and the entry fields will be smaller in size ... since they will not need to be "thumb friendly".

Show/Hide Popup Keypads:

Select Show or Hide to show or hide the popup keypad icons located next to numeric entry fields. These are generally only needed for mobile devices that don't have decimal points in their numeric keypads. So if you are on a desktop, you may find the calculator to be more user-friendly and less cluttered without them.

Stick/Unstick Tools:

Select Stick or Unstick to stick or unstick the help and tools panel. Selecting "Stick" will keep the panel in view while scrolling the calculator vertically. If you find that annoying, select "Unstick" to keep the panel in a stationary position.

If the tools panel becomes "Unstuck" on its own, try clicking "Unstick" and then "Stick" to re-stick the panel.