Online Triangle Calculator

Interactive Triangle calculator

The triangle calculator calculates the angles, heights, area, incircle radius, Circumcircle radius, ...

Move the points in the grafic or define the point coordinates in the numeric field to define the triangle. The calulated results are shown in the table. The calculation formulas are given below.

Scale:
Number of digits =
Side length:
a=
b=
c=
Heigths:
ha=
hb=
hc=
Angles in degree:
α=
β=
γ=
Angles in radian:
α=
β=
γ=
Median lines:
ma=
mb=
mc=
Bisector lines:
lα=
lβ=
lγ=
Circum­ference U=
Area =
Circle radii
R=
r=

Axes ranges

x-min=
x-max=
y-min=
y-max=

Definition of the triangle:

Point 1 coordinates x, y

P1 =

Point 2 coordinates x, y

P2 =

Point 3 coordinates x, y

P3 =

Side length

a=
b=
c=

Angle

α=
β=
γ=

Styles for the fgrafic and selection of the displayed elements:

P1, P2, P3:
Sides:
Incircle:
Circumcircle:
Heights:
Median lines:
Perpendicular lines:
Bisector lines:

Triangle calculation formulas

Angular sum

The angle sum in triangle is 180°.

α+β+γ=180°

Median

triangle-median

By a median is meant a straight line connecting a vertex of the triangle to the center of the opposite side. The sides of a triangle intersect at the center of gravity of the triangle.

The length of the median of side a is:

ma=2b2+c2-a22

The length of the median of side b is:

mb=2a2+c2-b22

The length of the median of side c is:

mc=2a2+b2-c22

Bisecting

triangle-bisection

A bisector is a straight line which divides an angle of the triangle into two equal parts. The bisectors of a triangle intersect at the center of the incircle.

The length of the bisector of the angle α is:

lα=bcb+c2-a2b+c

The length of the bisector of the angle β is:

lβ=aca+c2-b2a+c

The length of the bisector of the angle γ is:

lγ=bab+a2-c2b+a

Height

triangle-heights

The height is defined as a straight line at 90° on one side and connecting the side to the opposite corner. The diagram shows the three heights in black dotted lines.

The length of the height on the side a is:

ha=bsinγ=csinβ

The length of the height on the side b is:

hb=asinγ=csinα

The length of the height on the side c is:

hc=asinβ=bsinα

Perpendicular bisector

triangle-perpendicular-lines

A perpendicular of a side is a line that divides one side of the triangle into two equal parts and is perpendicular to the side. The perpendicular bisector lines of a triangle intersect at the center of the circumcircle.

Circumcircle radius r

The circumcircle is a circle passing through the vertices of the triangle.

r=s4cosα2cosβ2cosγ2

with

s=12a+b+c

Incircle radius ρ

The incircle is a circle that touches each side of the triangle.

ρ=s-as-bs-cs

Triangle area A

The formula for the triangle area is:

A=12absinγ

Triangle circumference U

The formula for the triangle circumference is:

U=a+b+c

Heronische area formula

The Heron formula for the triangle area is:

A=ρs=ss-as-bs-c

Center line

The center line connects the centers of two triangle sides. It is parallel to the third side and half as long.

Rectangular triangle

The cathetes a and b form a right angle. In oposite to the right angle is the hypotenuse c. The theorem of Pythagoras holds:

c2=a2+b2

Area A in the rectangular triangle

The formula for the triangle area in a right angle triangle is:

A=ab2

Essential for the calculations in general triangle are the cosine and the sine law and the relationship of the trigonometric functions.

Sine law

asinα=bsinβ=csinγ

Cosine law

a2=b2+c2-2bccosα

b2=a2+c2-2accosβ

c2=a2+b2-2abcosγ

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Releated sites

Here is a list of of further useful sites:

Index Trigonometric calculations Circle Ellipse Parallelogram Rectangle