Search
Mathematical tables: typical geometry related formulas
Tables show typical formulas related to geometry such as surface area of various geometric plane shapes, disk curcumference, sphere volume etc.

Beta version

BETA TEST VERSION OF THIS ITEM
This online calculator is currently under heavy development. It may or it may NOT work correctly.
You CAN try to use it. You CAN even get the proper results.
However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.
Feel free to send any ideas and comments !
⌛ Loading...

Disk and circle

NameFormulaLegend
Disk area surfaceShow sourceS:=πR2 S:=\pi\cdot{ R}^{2}
  • S - surface area of the disk,
  • R - disk radius (length of line segments from its center to its perimeter),
  • π\pi - pi number (math constant approximately equal to 3.14159).
Disk or circle circumferenceShow sourceL:=2 πR L:=2~\pi\cdot R
  • L - disk circumference (linear distance around circle or disk),
  • R - disk radius (length of line segments from its center to its perimeter),
  • π\pi - pi number (math constant approximately equal to 3.14159).
Disk radius from area surfaceShow sourceR:=Sπ R:=\sqrt{\frac{ S}{\pi}}
  • R - disk radius (length of line segments from its center to its perimeter),
  • S - surface area of the disk,
  • π\pi - pi number (math constant approximately equal to 3.14159).
Disk radius from areaShow sourceL:=2 πS L:=2~\sqrt{\pi\cdot S}
  • L - disk circumference (linear distance around circle or disk),
  • S - surface area of the disk,
  • π\pi - pi number (math constant approximately equal to 3.14159).
Disk (circle) circumference from circumferenceShow sourceR:=L2 π R:=\frac{ L}{2~\pi}
  • R - disk radius (length of line segments from its center to its perimeter),
  • L - disk circumference (linear distance around circle or disk),
  • π\pi - pi number (math constant approximately equal to 3.14159).
Disk (circle) area from circumferenceShow sourceS:=L24 π S:=\frac{{ L}^{2}}{4~\pi}
  • S - surface area of the disk,
  • L - disk circumference (linear distance around circle or disk),
  • π\pi - pi number (math constant approximately equal to 3.14159).

Surface areas of plane shapes

NameFormulaLegend
Disk area surfaceShow sourceS:=πR2 S:=\pi\cdot{ R}^{2}
  • S - surface area of the disk,
  • R - disk radius (length of line segments from its center to its perimeter),
  • π\pi - pi number (math constant approximately equal to 3.14159).
Parallelogram areaShow sourceS:=ah S:= a\cdot h
  • S - area of the parallelogram,
  • a - length of the parallelogram base,
  • h - height of the parallelogram.
Rectangle areaShow sourceS:=ab S:= a\cdot b
  • S - area of the rectangle,
  • a - length of the first rectangle side,
  • b - length of the second rectangle side.
Rectangle diagonalShow sourced:=a2+b2 d:=\sqrt{{ a}^{2}+{ b}^{2}}
  • d - length of the rectangle diagonal,
  • a - length of the first rectangle side,
  • b - length of the second rectangle side.
Rectangle area from diagonalShow sourceS:=12d2sin(α) S:=\frac{1}{2}\cdot{ d}^{2}\cdot\sin\left( \alpha\right)
  • S - area of the rectangle,
  • d - length of the rectangle diagonal,
  • α\alpha - smaller angle between rectangle diagonals.
Rhombus areaShow sourceS:=12ef S:=\frac{1}{2}\cdot e\cdot f
  • S - area of the rhombus,
  • e - length of the first rhombus diagonal,
  • f - length of the second rhombus diagonal.
Square areaShow sourceS:=a2 S:={ a}^{2}
  • S - area of the square,
  • a - length of the square side.
Square area from diagonalShow sourceS:=d22 S:=\frac{{ d}^{2}}{2}
  • S - area of the square,
  • d - length of the square diagonal.
Trapezoid areaShow sourceS:=(a+b)2h S:=\frac{\left( a+ b\right)}{2}\cdot h
  • S - area of the trapezoid,
  • a - length of the first trapezoid base,
  • b - length of the second trapezoid base,
  • h - height of the trapezoid.
Triangle area (general)Show sourceS:=12ah S:=\frac{1}{2}\cdot a\cdot h
  • S - area of the triangle,
  • a - length of the triangle base,
  • h - height of the triangle.
Equilateral triangle areaShow sourceS:=a32 S:=\frac{ a\cdot\sqrt{3}}{2}
  • S - area of the equilateral triangle,
  • a - length of the equilateral triangle side.
Isosceles triangle areaShow sourceS:=b44 a2b2 S:=\frac{ b}{4}\cdot\sqrt{4~{ a}^{2}-{ b}^{2}}
  • S - area of the isosceles triangle,
  • a - length of the isosceles triangle base,
  • b - length of the isosceles triangle side.

Circumference of shapes

NameFormulaLegend
Disk or circle circumferenceShow sourceL:=2 πR L:=2~\pi\cdot R
  • L - disk circumference (linear distance around circle or disk),
  • R - disk radius (length of line segments from its center to its perimeter),
  • π\pi - pi number (math constant approximately equal to 3.14159).
Parallelogram circumferenceShow sourceL:=2(a+b) L:=2\cdot\left( a+ b\right)
  • L - circumference of the parallelogram,
  • a - length of the first parallelogram side,
  • b - length of the second parallelogram side.
Rectangle circumferenceShow sourceL:=2(a+b) L:=2\cdot\left( a+ b\right)
  • L - circumference of the rectangle,
  • a - length of the first rectangle side,
  • b - length of the second rectangle side.
Rhombus circumferenceShow sourceL:=4a L:=4\cdot a
  • L - circumference of the rhombus,
  • a - length of the rhombus side.
Square circumferenceShow sourceL:=4a L:=4\cdot a
  • L - circumference of the square,
  • a - length of the square side.
Triangle circumference (general)Show sourceL:=a+b+c L:= a+ b+ c
  • L - circumference of the triangle,
  • a - length of the triangle first side,
  • b - length of the triangle second side,
  • c - length of the triangle third side.
Equilateral triangle circumferenceShow sourceL:=3a L:=3\cdot a
  • L - circumference of the equilateral triangle,
  • a - length of the equilateral triangle side.
Isosceles triangle circumferenceShow sourceL:=a+2b L:= a+2\cdot b
  • L - circumference of the isosceles triangle,
  • a - length of the isosceles triangle base,
  • b - length of the isosceles triangle side.

Parallelogram

NameFormulaLegend
Parallelogram areaShow sourceS:=ah S:= a\cdot h
  • S - area of the parallelogram,
  • a - length of the parallelogram base,
  • h - height of the parallelogram.
Parallelogram circumferenceShow sourceL:=2(a+b) L:=2\cdot\left( a+ b\right)
  • L - circumference of the parallelogram,
  • a - length of the first parallelogram side,
  • b - length of the second parallelogram side.

Renctangle

NameFormulaLegend
Rectangle areaShow sourceS:=ab S:= a\cdot b
  • S - area of the rectangle,
  • a - length of the first rectangle side,
  • b - length of the second rectangle side.
Rectangle circumferenceShow sourceL:=2(a+b) L:=2\cdot\left( a+ b\right)
  • L - circumference of the rectangle,
  • a - length of the first rectangle side,
  • b - length of the second rectangle side.
Rectangle diagonalShow sourced:=a2+b2 d:=\sqrt{{ a}^{2}+{ b}^{2}}
  • d - length of the rectangle diagonal,
  • a - length of the first rectangle side,
  • b - length of the second rectangle side.
Rectangle area from diagonalShow sourceS:=12d2sin(α) S:=\frac{1}{2}\cdot{ d}^{2}\cdot\sin\left( \alpha\right)
  • S - area of the rectangle,
  • d - length of the rectangle diagonal,
  • α\alpha - smaller angle between rectangle diagonals.

Rhombus

NameFormulaLegend
Rhombus areaShow sourceS:=12ef S:=\frac{1}{2}\cdot e\cdot f
  • S - area of the rhombus,
  • e - length of the first rhombus diagonal,
  • f - length of the second rhombus diagonal.
Rhombus circumferenceShow sourceL:=4a L:=4\cdot a
  • L - circumference of the rhombus,
  • a - length of the rhombus side.

Square

NameFormulaLegend
Square areaShow sourceS:=a2 S:={ a}^{2}
  • S - area of the square,
  • a - length of the square side.
Square circumferenceShow sourceL:=4a L:=4\cdot a
  • L - circumference of the square,
  • a - length of the square side.
Square diagonalShow sourced:=a 2 d:= a~\sqrt{2}
  • d - length of the square diagonal,
  • a - length of the square side.
Square area from diagonalShow sourceS:=d22 S:=\frac{{ d}^{2}}{2}
  • S - area of the square,
  • d - length of the square diagonal.

Trapezoid

NameFormulaLegend
Trapezoid areaShow sourceS:=(a+b)2h S:=\frac{\left( a+ b\right)}{2}\cdot h
  • S - area of the trapezoid,
  • a - length of the first trapezoid base,
  • b - length of the second trapezoid base,
  • h - height of the trapezoid.

Triangle

NameFormulaLegend
Triangle area (general)Show sourceS:=12ah S:=\frac{1}{2}\cdot a\cdot h
  • S - area of the triangle,
  • a - length of the triangle base,
  • h - height of the triangle.
Triangle circumference (general)Show sourceL:=a+b+c L:= a+ b+ c
  • L - circumference of the triangle,
  • a - length of the triangle first side,
  • b - length of the triangle second side,
  • c - length of the triangle third side.
Equilateral triangle areaShow sourceS:=a32 S:=\frac{ a\cdot\sqrt{3}}{2}
  • S - area of the equilateral triangle,
  • a - length of the equilateral triangle side.
Equilateral triangle circumferenceShow sourceL:=3a L:=3\cdot a
  • L - circumference of the equilateral triangle,
  • a - length of the equilateral triangle side.
Isosceles triangle areaShow sourceS:=b44 a2b2 S:=\frac{ b}{4}\cdot\sqrt{4~{ a}^{2}-{ b}^{2}}
  • S - area of the isosceles triangle,
  • a - length of the isosceles triangle base,
  • b - length of the isosceles triangle side.
Isosceles triangle circumferenceShow sourceL:=a+2b L:= a+2\cdot b
  • L - circumference of the isosceles triangle,
  • a - length of the isosceles triangle base,
  • b - length of the isosceles triangle side.

Equilateral triangle

NameFormulaLegend
Equilateral triangle areaShow sourceS:=a32 S:=\frac{ a\cdot\sqrt{3}}{2}
  • S - area of the equilateral triangle,
  • a - length of the equilateral triangle side.
Equilateral triangle circumferenceShow sourceL:=3a L:=3\cdot a
  • L - circumference of the equilateral triangle,
  • a - length of the equilateral triangle side.

Isosceles triangle

NameFormulaLegend
Isosceles triangle areaShow sourceS:=b44 a2b2 S:=\frac{ b}{4}\cdot\sqrt{4~{ a}^{2}-{ b}^{2}}
  • S - area of the isosceles triangle,
  • a - length of the isosceles triangle base,
  • b - length of the isosceles triangle side.
Isosceles triangle circumferenceShow sourceL:=a+2b L:= a+2\cdot b
  • L - circumference of the isosceles triangle,
  • a - length of the isosceles triangle base,
  • b - length of the isosceles triangle side.

Some facts

  • Geometry is one of two oldest fields of mathematics (next to arithmetic).
  • Geometry examines geometric shapes and their relationships.
  • Due to the kind of shapes we deal with, we divide the geometry into two parts:
    • planimetry - the part dealing with flat shapes, i.e. those that can be drawn in a 2D plane like square, circle, etc.,
    • stereometry - the part dealing with spatial solids, i.e. three-dimensional shapes such as cube or cylinder.
  • The origins of geometry go back to ancient times. The father of geometry in the form we know today is Greek philosopher Euclid. About 300 BC he prioritized knowledge about geometry, which resulted in a dissertation "Elements".
  • Euclid's "Elements" are considered one of the first theoretical works in mathematics. Euclid, ordering the previous knowledge, indicated a few the most basic laws (so-called axioms), and then he used them to derive all existing geometry as today's mathematicians do. This is why his work is considered a breakthrough not only for the development of geometry, but mathematics in general.
  • The axioms adopted by Euclid were as follows:
    • 1. To draw a straight line from any point to any point.
    • 2. To produce a finite straight line continuously in a straight line.
    • 3. To describe a circle with any centre and distance.
    • 4. That all right angles are equal to one another.
    • 5. That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than two right angles.
  • Nowadays, geometry based on the above postulates is called Euclidean geometry. However, over time, mathematicians began to study geometries based on other axioms, removing or modifying selected points from the original list used by Euclid. Such geometries are, for example, Riemann's geometry (removing the Euclidian postulate 5.), used to formulate General relativity of Einstein or so-called pointless geometry.

Tags and links to this website

What tags this calculator has

Permalink

This is permalink. Permalink is the link containing your input data. Just copy it and share your work with friends:

Links to external sites (leaving Calculla?)

JavaScript failed !
So this is static version of this website.
This website works a lot better in JavaScript enabled browser.
Please enable JavaScript.