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Geometry Formulas
Browse 7 reviewed geometry formulas with concrete inputs, outputs, calculations, applicability checks, and LaTeX.
Geometry
Area of a Circle
A=\pi r^2Calculates the area enclosed by a circle of radius r.
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Area of a Triangle
A=\frac{1}{2}bhCalculates triangle area from a base and its perpendicular height.
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Circumference of a Circle
C=2\pi r=\pi dCalculates the distance around a circle from its radius or diameter.
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Haversine Distance
d=2R\arcsin\sqrt{\sin^2\frac{\Delta\varphi}{2}+\cos\varphi_1\cos\varphi_2\sin^2\frac{\Delta\lambda}{2}}Approximates great-circle distance between two latitude–longitude points on a sphere.
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Law of Sines
\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}Relates each side of a triangle to the sine of its opposite angle.
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Pythagorean Theorem
a^2+b^2=c^2Relates the side lengths of a right triangle.
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Volume of a Sphere
V=\frac{4}{3}\pi r^3Calculates the volume enclosed by a sphere.
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Geometry
Arc Length from a Radian Angle
s=r\thetaCalculates the length of a circular arc from radius and angle in radians.
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Area of a Circular Sector
A=\frac12 r^2\thetaCalculates sector area when the central angle is measured in radians.
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Area of an Ellipse
A=\pi abCalculates the area enclosed by an ellipse from its semi-major and semi-minor axes.
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Circular Arc Length
s=r\thetaCalculates an arc length from a circle radius and a central angle measured in radians.
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Circular Arc Length
s=r\thetaComputes circular arc length when the angle is measured in radians.
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Cone Volume
V=\frac{1}{3}\pi r^2hCalculates the volume of a right circular cone.
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Cylinder Volume
V=\pi r^2hCalculates the volume of a right circular cylinder.
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Distance Between Two Points in 3D
d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}Computes Euclidean distance between two points in three-dimensional space.
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Heron Formula
A=\sqrt{s(s-a)(s-b)(s-c)},\quad s=\frac{a+b+c}{2}Calculates triangle area from its three side lengths.
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Law of Cosines
c^2=a^2+b^2-2ab\cos CRelates the sides of any triangle to the cosine of one included angle.
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Midpoint Formula
M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)Finds the point halfway between two coordinate points.
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Parallelogram Area
A=bhCalculates area from a base and perpendicular height.
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Rectangle Area
A=lwCalculates the area of a rectangle.
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Rectangle Perimeter
P=2(l+w)Calculates the perimeter of a rectangle.
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Rectangular Prism Volume
V=lwhCalculates volume from length, width, and height.
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Sphere Surface Area
A=4\pi r^2Calculates the surface area of a sphere.
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Total Surface Area of a Cylinder
S=2\pi r^2+2\pi rhAdds the areas of two circular bases and the curved lateral surface.
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Trapezoid Area
A=\frac{1}{2}(b_1+b_2)hCalculates area from parallel bases and height.
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