Triangle Calculator to Solve SSS, SAS, SSA, ASA, and AAS Triangles

Triangle Calculator Sign

This triangle solver will take three known triangle measurements and solve for the other three.

The calculator will also solve for the area of the triangle, the perimeter, the semi-perimeter, the radius of the circumcircle and the inscribed circle, the medians, and the heights.

Plus, unlike other online triangle calculators, this calculator will show its work by detailing each of the steps it took to solve the formulas for finding the missing values.

Finally, the triangle calculator will also calculate the coordinates of the vertices, the centroid, and the circumcenter, and draw the solved triangle based on those coordinates (requires latest version of your web browser software).

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Triangle Calculator

Solve triangles given SSS, SAS, SSA, ASA, or AAS.

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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 solving the triangle.

Angles in:Angles stated in:Angles stated in:Angles stated in:

Angles stated in:

Select whether you will be entering angle values as degrees or radians.

Known values:

Known values:

Select the radio button that indicates which three of the triangle values are known. Upon making your selection the triangle calculator will load the appropriate entry form.

SSS - 3 side lengths

SAS - 2 sides and the included angle given

SSA - 2 sides and non-included angle given

ASA - a side and 2 adjacent angles

AAS - a side, 1 adjacent angle, and the opposite angle

SSS: Enter the 3 SidesTriangle diagram SSS
Side a:Side aSide a length:Side a length:

Side a length:

Enter the length of side a.

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Side b:Side bSide b length:Side b length:

Side b length:

Enter the length of side b.

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Side c:Side cSide c length:Side c length:

Side c length:

Enter the length of side c.

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TriangleSolution
TypeTypeClassificationClassification

Triangle classification:

This is the type of triangle based on the entered and computed triangle values.

Side aSide aSide aSide a

Side a:

This is the length of side a of the solved triangle.

Side bSide bSide bSide b

Side b:

This is the length of side b of the solved triangle.

Side cSide cSide cSide c

Side c:

This is the length of side c of the solved triangle.

Angle AAngle AAngle AAngle A

Angle A:

This is the angle of vertex A of the solved triangle.

Angle BAngle BAngle BAngle B

Angle B:

This is the angle of vertex B of the solved triangle.

Angle CAngle CAngle CAngle C

Angle C:

This is the angle of vertex C of the solved triangle.

PPPerimeterPerimeter

Perimeter:

This is the perimeter (P) of the solved triangle. The formula used is P = a + b + c.

ssSemi-perimeterSemi-perimeter

Semi-perimeter:

This is the semi-perimeter (s) of the solved triangle. The formula used is s = (a + b + c) / 2.

AreaAreaAreaArea

Area:

This is the area (K) of the solved triangle. The formula used is K = (base x height) / 2.

Radius rRadius rRadius of inscribed circleRadius of inscribed circle

Radius of inscribed circle:

This is the radius (r) of the inscribed circle of the solved triangle. The inscribed circle is the largest circle that will fit within the triangle. The formula used to find the radius is, r = sqrt[ ((s-a)(s-b)(s-c)) / s], where s is the semi-perimeter of the triangle.

Radius RRadius RRadius of circumscribed circleRadius of circumscribed circle

Radius of circumscribed circle:

This is the radius (R) of the circumscribed circle of the solved triangle. The circumscribed circle is a circle that passes through all three vertices of a triangle. The formula used to find the radius is, R = (abc) / (4K), where K is the area of the triangle.

mamaMedian maMedian ma

Median ma:

This is the length of the median (ma), which is the line that runs from vertex A to the mid-point of side a (the opposite side). The formula used for finding the length of the line is, ma = (1/2)sqrt[2c2 + 2b2 - a2].

mbmbMedian mbMedian mb

Median mb:

This is the length of the median (mb), which is the line that runs from vertex B to the mid-point of side b (the opposite side). The formula used for finding the length of the line is, mb = (1/2)sqrt[2c2 + 2a2 - b2].

mcmcMedian mcMedian mc

Median mc:

This is the length of the median (mc), which is the line that runs from vertex C to the mid-point of side c (the opposite side). The formula used for finding the length of the line is, mc = (1/2)sqrt[2a2 + 2b2 - c2].

hahaHeight haHeight ha

Height ha:

This is the height (h) of the triangle using side a as the base. The formula used to find the height is, ha = 2 * (K / a), where K is the area of the triangle.

hbhbHeight hbHeight hb

Height hb:

This is the height (h) of the triangle using side b as the base. The formula used to find the height is, hb = 2 * (K / b), where K is the area of the triangle.

hchcHeight hcHeight hc

Height hc:

This is the height (h) of the triangle using side c as the base. The formula used to find the height is, hc = 2 * (K / c), where K is the area of the triangle.

A coordA coordA coordVertex A coordinate

Vertex A coordinate:

This is the coordinate used for vertex A. In order to plot the triangle for drawing, vertex A is always located at coordinate [0,0].

B coordB coordB coordVertex B coordinate

Vertex B coordinate:

This is the coordinate used for vertex B. In order to plot the triangle for drawing, the y coordinate of vertex B is always 0. The x coordinate of vertex B is always equal to the length of side c.

C coordC coordC coordVertex C coordinate

Vertex C coordinate:

This is the coordinate used for vertex C. The calculations used to find the x and y coordinates of vertex C are as follows:
ca = (b2 - a2 + c2) / (2 * c)
ch = sqrt[b2 - ca2]
cx2 = 0 + (ca * (c - 0)) / c
Cx = cx2 + (ch * ( 0 - 0 ) / c)
cy2 = 0 + (ca * (0 - 0)) / c
Cy = cy2 + (ch * ( c - 0 ) / c)

CentroidCentroidCentroid coord.Centroid coordinate

Centroid coordinate:

This is the centroid coordinate based on the three vertex coordinates. The formula used is:
Centroid x = 1/3(Ax + Bx + Cx)
Centroid y = 1/3(Ay + By + Cy)

CC coordCC coordCircumcenter coord.Circumcenter coordinate

Circumcenter coordinate:

This is the circumcenter coordinate based on the three vertex coordinates. The formula used is:
D = 2(BxCy - ByCx)
Ux = Cy(Bx2 + By2) - By(Cx2 + Cy2) / D
Uy = Bx(Cx2 + Cy2) - Cx(Bx2 + By2) / D

I will show my work here:

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

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.