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Rectangle Area
A rectangle partitions into equal rows and columns of square units.
Open calculator ↗Rectangle Perimeter
Perimeter measures the full boundary of a rectangle.
Open calculator ↗Rectangle Diagonal
The diagonal joins opposite corners and forms a right triangle with the two sides.
Open calculator ↗Square Area
A square has two equal perpendicular dimensions.
Open calculator ↗Square Perimeter
A square has four equal edges, so one side determines the full boundary.
Open calculator ↗Square Diagonal
A square diagonal is the hypotenuse of an isosceles right triangle.
Open calculator ↗Circle Area
Circle area depends on the square of the distance from the centre to the boundary.
Open calculator ↗Circle Circumference
The circumference is the length around a circle.
Open calculator ↗Circle Radius from Area
Inverting the circle-area relation recovers a radius from a known surface area.
Open calculator ↗Circle Diameter from Circumference
The ratio of a circle's circumference to its diameter is constant, so division by pi reverses the measurement.
Open calculator ↗Triangle Area
A triangle fills half a parallelogram with the same base and perpendicular height.
Open calculator ↗Heron Triangle Area
Heron's formula finds triangle area from the three side lengths alone.
Open calculator ↗Right Triangle Hypotenuse
The hypotenuse sits opposite the right angle and is always the longest side of a right triangle.
Open calculator ↗Missing Right Triangle Leg
Rearranging Pythagoras finds the missing perpendicular leg when the longest side and one leg are known.
Open calculator ↗Equilateral Triangle Area
An equilateral triangle divides into two matching right triangles, which explains the square-root-of-three factor.
Open calculator ↗Equilateral Triangle Height
The altitude of an equilateral triangle bisects its base and forms a thirty-sixty-ninety triangle.
Open calculator ↗Triangle Third Angle
Interior angles of a Euclidean triangle sum to one hundred eighty degrees.
Open calculator ↗Law of Cosines Side
The law of cosines extends the right-triangle relation to any included angle.
Open calculator ↗Parallelogram Area
Sliding a corner triangle to the other side turns a parallelogram into a rectangle without changing its area.
Open calculator ↗Trapezoid Area
A trapezoid's average parallel width multiplied by its perpendicular height gives the enclosed area.
Open calculator ↗Rhombus Area
The perpendicular diagonals of a rhombus split it into four right triangles.
Open calculator ↗Ellipse Area
An ellipse can be viewed as a circle stretched independently along two perpendicular axes.
Open calculator ↗Ellipse Perimeter Estimate
Ramanujan's first perimeter approximation gives a convenient estimate without evaluating an elliptic integral.
Open calculator ↗Sector Area
A sector is a fraction of a circle selected by its central angle.
Open calculator ↗Arc Length
Arc length measures the curved boundary selected by a central angle.
Open calculator ↗Chord Length
A chord is the straight segment between two points on a circle.
Open calculator ↗Annulus Area
An annulus is the ring left after removing a concentric smaller disk.
Open calculator ↗Regular Polygon Area
A regular polygon splits into congruent triangles around its centre.
Open calculator ↗Regular Polygon Interior Angle
A regular polygon shares its total interior angle sum evenly across its vertices.
Open calculator ↗Polygon Diagonal Count
Each vertex connects by diagonals to all except itself and its two neighbours.
Open calculator ↗Cube Volume
A cube stacks equal square layers through its depth.
Open calculator ↗Cube Surface Area
Six identical square faces form the outside of a closed cube.
Open calculator ↗Cuboid Volume
Three perpendicular dimensions determine the capacity of a rectangular box.
Open calculator ↗Cuboid Surface Area
A cuboid has three pairs of matching rectangular faces.
Open calculator ↗Cuboid Space Diagonal
The space diagonal connects opposite vertices through the interior of the box.
Open calculator ↗Cylinder Volume
A right circular cylinder has a constant disk-shaped cross-section along its height.
Open calculator ↗Cylinder Total Surface Area
Two disks and one unrolled rectangular side make up a closed cylinder's surface.
Open calculator ↗Cone Volume
A cone occupies one third of a cylinder with the same base and perpendicular height.
Open calculator ↗Cone Slant Height
The side length of a right cone forms a right triangle with its radius and vertical height.
Open calculator ↗Cone Total Surface Area
The total combines a circular base with the curved lateral surface.
Open calculator ↗Sphere Volume
Sphere volume scales with the cube of radius.
Open calculator ↗Sphere Surface Area
The surface of a sphere has four times the area of its great-circle disk.
Open calculator ↗Hemisphere Volume
A hemisphere is one half of a sphere cut through its centre.
Open calculator ↗Square Pyramid Volume
A square pyramid uses one third of its base-area prism volume.
Open calculator ↗Conical Frustum Volume
A frustum describes a cone with its tip removed by a parallel cut.
Open calculator ↗Distance Between 2D Points
Euclidean distance combines perpendicular coordinate differences.
Open calculator ↗Distance Between 3D Points
Three-dimensional distance extends the same right-angle relation to three orthogonal axes.
Open calculator ↗Degrees to Radians
Radians express angle as arc length divided by radius.
Open calculator ↗Radians to Degrees
Converting to degrees expresses an angle in three hundred sixty parts per turn.
Open calculator ↗Scale Model Length
A one-to-n model reduces every real length by the scale denominator.
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