Tables show typical formulas related to geometry such as surface area of various geometric plane shapes, disk circumference, 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#

Name	Formula	Legend
Disk area surface	Show source $S=\pi \cdot R^{2}$	S - surface area of the disk, R - disk radius (length of line segments from its center to its perimeter), $\pi$ - pi number (math constant approximately equal to 3.14159).
Disk or circle circumference	Show source $L=2~\pi \cdot R$	L - disk circumference (linear distance around circle or disk), R - disk radius (length of line segments from its center to its perimeter), $\pi$ - pi number (math constant approximately equal to 3.14159).
Disk radius from area surface	Show source $R=\sqrt{\frac{S}{\pi}}$	R - disk radius (length of line segments from its center to its perimeter), S - surface area of the disk, $\pi$ - pi number (math constant approximately equal to 3.14159).
Disk radius from area	Show source $L=2 \cdot \sqrt{\pi \cdot S}$	L - disk circumference (linear distance around circle or disk), S - surface area of the disk, $\pi$ - pi number (math constant approximately equal to 3.14159).
Disk (circle) circumference from circumference	Show source $R=\frac{L}{2~\pi}$	R - disk radius (length of line segments from its center to its perimeter), L - disk circumference (linear distance around circle or disk), $\pi$ - pi number (math constant approximately equal to 3.14159).
Disk (circle) area from circumference	Show source $S=\frac{L^{2}}{4~\pi}$	S - surface area of the disk, L - disk circumference (linear distance around circle or disk), $\pi$ - pi number (math constant approximately equal to 3.14159).

Surface areas of plane shapes#

Name	Formula	Legend
Disk area surface	Show source $S=\pi \cdot R^{2}$	S - surface area of the disk, R - disk radius (length of line segments from its center to its perimeter), $\pi$ - pi number (math constant approximately equal to 3.14159).
Parallelogram area	Show source $S=a \cdot h$	S - area of the parallelogram, a - length of the parallelogram base, h - height of the parallelogram.
Rectangle area	Show source $S=a \cdot b$	S - area of the rectangle, a - length of the first rectangle side, b - length of the second rectangle side.
Rectangle diagonal	Show source $d=\sqrt{a^{2}+b^{2}}$	d - length of the rectangle diagonal, a - length of the first rectangle side, b - length of the second rectangle side.
Rectangle area from diagonal	Show source $S=\frac{1}{2}~d^{2} \cdot sin\left(\alpha\right)$	S - area of the rectangle, d - length of the rectangle diagonal, $\alpha$ - smaller angle between rectangle diagonals.
Rhombus area	Show source $S=\frac{1}{2}~e \cdot f$	S - area of the rhombus, e - length of the first rhombus diagonal, f - length of the second rhombus diagonal.
Square area	Show source $S=a^{2}$	S - area of the square, a - length of the square side.
Square area from diagonal	Show source $S=\frac{d^{2}}{2}$	S - area of the square, d - length of the square diagonal.
Trapezoid area	Show source $S=\frac{a+b}{2} \cdot h$	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 source $S=\frac{1}{2}~a \cdot h$	S - area of the triangle, a - length of the triangle base, h - height of the triangle.
Equilateral triangle area	Show source $S=\frac{a \cdot \sqrt{3}}{2}$	S - area of the equilateral triangle, a - length of the equilateral triangle side.
Isosceles triangle area	Show source $S=\frac{b}{4} \cdot \sqrt{4~a^{2}-b^{2}}$	S - area of the isosceles triangle, a - length of the isosceles triangle base, b - length of the isosceles triangle side.

Circumference of shapes#

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

Parallelogram#

Name	Formula	Legend
Parallelogram area	Show source $S=a \cdot h$	S - area of the parallelogram, a - length of the parallelogram base, h - height of the parallelogram.
Parallelogram circumference	Show source $L=2~\left(a+b\right)$	L - circumference of the parallelogram, a - length of the first parallelogram side, b - length of the second parallelogram side.

Renctangle#

Name	Formula	Legend
Rectangle area	Show source $S=a \cdot b$	S - area of the rectangle, a - length of the first rectangle side, b - length of the second rectangle side.
Rectangle circumference	Show source $L=2~\left(a+b\right)$	L - circumference of the rectangle, a - length of the first rectangle side, b - length of the second rectangle side.
Rectangle diagonal	Show source $d=\sqrt{a^{2}+b^{2}}$	d - length of the rectangle diagonal, a - length of the first rectangle side, b - length of the second rectangle side.
Rectangle area from diagonal	Show source $S=\frac{1}{2}~d^{2} \cdot sin\left(\alpha\right)$	S - area of the rectangle, d - length of the rectangle diagonal, $\alpha$ - smaller angle between rectangle diagonals.

Rhombus#

Name	Formula	Legend
Rhombus area	Show source $S=\frac{1}{2}~e \cdot f$	S - area of the rhombus, e - length of the first rhombus diagonal, f - length of the second rhombus diagonal.
Rhombus circumference	Show source $L=4~a$	L - circumference of the rhombus, a - length of the rhombus side.

Square#

Name	Formula	Legend
Square area	Show source $S=a^{2}$	S - area of the square, a - length of the square side.
Square circumference	Show source $L=4~a$	L - circumference of the square, a - length of the square side.
Square diagonal	Show source $d=a \cdot \sqrt{2}$	d - length of the square diagonal, a - length of the square side.
Square area from diagonal	Show source $S=\frac{d^{2}}{2}$	S - area of the square, d - length of the square diagonal.

Trapezoid#

Name	Formula	Legend
Trapezoid area	Show source $S=\frac{a+b}{2} \cdot h$	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#

Name	Formula	Legend
Triangle area (general)	Show source $S=\frac{1}{2}~a \cdot h$	S - area of the triangle, a - length of the triangle base, h - height of the triangle.
Triangle circumference (general)	Show source $L=a+b+c$	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 area	Show source $S=\frac{a \cdot \sqrt{3}}{2}$	S - area of the equilateral triangle, a - length of the equilateral triangle side.
Equilateral triangle circumference	Show source $L=3~a$	L - circumference of the equilateral triangle, a - length of the equilateral triangle side.
Isosceles triangle area	Show source $S=\frac{b}{4} \cdot \sqrt{4~a^{2}-b^{2}}$	S - area of the isosceles triangle, a - length of the isosceles triangle base, b - length of the isosceles triangle side.
Isosceles triangle circumference	Show source $L=a+2~b$	L - circumference of the isosceles triangle, a - length of the isosceles triangle base, b - length of the isosceles triangle side.

Equilateral triangle#

Name	Formula	Legend
Equilateral triangle area	Show source $S=\frac{a \cdot \sqrt{3}}{2}$	S - area of the equilateral triangle, a - length of the equilateral triangle side.
Equilateral triangle circumference	Show source $L=3~a$	L - circumference of the equilateral triangle, a - length of the equilateral triangle side.

Isosceles triangle#

Name	Formula	Legend
Isosceles triangle area	Show source $S=\frac{b}{4} \cdot \sqrt{4~a^{2}-b^{2}}$	S - area of the isosceles triangle, a - length of the isosceles triangle base, b - length of the isosceles triangle side.
Isosceles triangle circumference	Show source $L=a+2~b$	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#

Tags:

mathematical_tables_geometry · table_of_formulas_for_geometry · geometric_formulas · geometry_related_formulas · surface_area_formulas

Tags to Polish version:

tablice_matematyczne_geometria · wzory_geometryczne · wzory_zwiazane_z_geometria · wzory_na_pola_figur

What tags this calculator has#

TABLE · MATH · A -> Z (all)

Permalink#

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

https://calculla.com/mathematical_tables_geometry

Links to external sites (leaving Calculla?)#