Geometry Calculators for Angles, Shapes and Vectors

Use these geometry calculators to work through questions about angles, shapes, perspective and vectors. Find an ellipse’s eccentricity, check whether three lengths can form a triangle, or calculate an angle bisector. The Distance Perspective Projection calculator helps with spatial measurements, while the 2D Vector Angle and 3D Vector Magnitude calculators support vector problems.These tools are useful for students checking homework, teachers preparing examples, and designers or engineers working with geometric measurements. Choose the calculator that matches your problem and enter the values you know.

Circle

Enter one known circle value — radius, diameter, circumference, or area — and instantly get all the other dimensions. Choose your preferred unit and the calculator does the rest.

Trigonometry

Calculate sin, cos and tan of any angle in degrees, radians or gradians — or enter a ratio and find the angle using arcsin, arccos or arctan.

3D Vector Magnitude

Find the length (magnitude) of any 3D vector instantly. Enter the x, y, and z components, and the calculator returns the Euclidean magnitude using the 3D Pythagorean theorem.

Angle Bisector

Enter the coefficients of two lines in general form (ax + by + c = 0) and this calculator finds the equations of both angle bisectors — the lines that divide the acute and obtuse angles formed where the lines meet.

Angular Size

Enter an object's linear size and its distance from the observer to find its angular size in degrees — the angle the object subtends in your field of view, as used in astronomy, optics, and photography.

Linear Size

Enter an object's angular size in degrees and its distance from the observer, and this Linear Size Calculator returns the object's actual linear size D using D = 2·L·tan(α/2). Useful for astronomy, optics, photography, and surveying.

Area

Calculate the area of a square, rectangle, triangle, circle, ellipse, trapezoid, regular polygon, ring and more. Pick a shape, enter its dimensions, and get the result in square meters, square feet, acres and hectares.

Length of the Angle Bisector

Enter the three side lengths of a triangle to find the length of the internal angle bisector — the segment that splits the angle between Side 1 and Side 2 into two equal parts.

Vertex of Quadratic Equation

Find the vertex of a quadratic equation y = ax² + bx + c instantly. Enter the coefficients a, b, and c, and the calculator returns the x and y coordinates of the parabola's turning point.

Distance Perspective Projection

Enter the linear size of an object and its angular size (in degrees) to find the distance at which the object must be placed so it appears under that angle. Uses the perspective projection formula L = D / (2·tan(α/2)).

2D Vector Magnitude

Enter the X and Y components of a two-dimensional vector to instantly find its magnitude (length) using the Pythagorean theorem. The result shows how far the vector extends from the origin.

Arc Length

Enter the radius and the central angle of a circle (in degrees, radians or gradians) and this calculator instantly returns the arc length using s = rθ, with the full calculation shown.

Volume

Volume calculator for 12 common 3D shapes: cube, box, cylinder, cone, sphere, hemisphere, pyramid, prism, capsule, frustum, ellipsoid and tube. Pick a shape, enter its dimensions, and get the volume in cubic units, liters and gallons.

2D Vector Angle

Enter the X and Y components of two vectors to find the angle between them in degrees. The calculator uses the dot product formula and is useful for physics, geometry, and computer graphics.

Cylinder Volume

Calculate the volume, height, or radius of a solid or hollow cylinder. Enter its dimensions or known volume, choose a length unit, and see surface areas and volume conversions.

Cone Volume and Surface Area

Calculate the volume, slant height, lateral area, base area and total surface area of a right circular cone. Enter the radius plus either the height or the slant height.

Surface Area

Calculate the total, lateral and base surface area of a cube, prism, cylinder, cone, sphere, hemisphere, pyramid, capsule or cone frustum. Pick a shape, enter its dimensions and get the area in the unit you choose.

Distance Between Two Points

Enter the coordinates of two points to get the straight-line distance between them, along with Δx, Δy and the midpoint of the segment. Supports meters, centimeters, feet and inches.

Midpoint

Find the midpoint of a line segment in 2D or 3D. Enter the coordinates of the two endpoints and get the midpoint plus the segment length instantly.

Right Triangle

Solve a right triangle from two known measurements, including at least one side. Enter side lengths, an acute angle, area, or perimeter to find the remaining measurements.

3D Vector Projection

Enter the components of two 3D vectors and this calculator projects one onto the other, showing the scalar projection, vector projection, perpendicular component, dot product, magnitudes, and the angle between the vectors.

Eccentricity of an Ellipse

Enter the semi-major axis (a) and semi-minor axis (b) of an ellipse to find its eccentricity (E) — a number between 0 and 1 that shows how elongated the ellipse is. Widely used in geometry, astronomy, and orbital mechanics.

2D Vector Subtraction

Subtract one 2D vector from another by entering the X and Y components of both vectors. The calculator performs component-wise subtraction and instantly shows the resulting vector's coordinates.

Cylinder Surface Area

Calculate the curved (lateral) surface area, base area, and total surface area of a cylinder from its radius and height. Supports m, cm, mm, ft and in, with step-by-step working shown.

Polygon Interior Angles

Enter the number of sides to find the sum of interior angles of any polygon. For a regular polygon you also get each interior angle and each exterior angle, with steps shown.

2D Vector Scalar Product

Enter the X and Y components of two vectors to compute their scalar (dot) product instantly. The result also tells you whether the angle between the vectors is acute, right, or obtuse.

Sector Area

Calculate the area of a circular sector from its radius and central angle. Enter the radius, choose units (deg, rad or grad), and get the sector area, arc length, perimeter and fraction of the full circle.

Sphere Volume and Surface Area

Calculate the volume, surface area, and great-circle circumference of a sphere from its radius or diameter. Enter one dimension, choose a unit, and get instant results with steps.

2D Vector Addition

Add two 2D vectors by entering their x and y components. The calculator returns the resulting vector's components instantly, ideal for physics, engineering, and math homework.

Distance from Point to Line

Enter the coordinates of a point and the coefficients of a line in the form Ax + By + C = 0 to find the shortest (perpendicular) distance between them, with full calculation steps.

Regular Polygon Area

Calculate the area of any regular polygon from its side length, apothem, or circumradius. Enter the number of sides and one known dimension to get the area, perimeter, and angles.

Triangle

Enter any three known values of a triangle — at least one side — and instantly get all three sides, all three angles, area, perimeter, heights, inradius, circumradius, plus a step-by-step solution and a scale drawing.

Pythagorean Theorem

Enter any two sides of a right triangle (legs a and b, or the hypotenuse c) and this calculator instantly finds the missing side, plus the area and perimeter.

Triangle Area

Calculate the area of a triangle from three side lengths (Heron's formula) or from a base and height. Enter your known values, pick a unit, and get the area with step-by-step calculations.

3D Vector Scalar Product

Calculate the scalar (dot) product of two 3D vectors instantly. Enter the X, Y and Z components of both vectors and get the result, which tells you how much the vectors align.

Triangle Inequality Checker

Check whether three side lengths can form a valid triangle. Enter the values for sides a, b, and c, and the calculator applies the Triangle Inequality Theorem to tell you if a triangle is possible.

3D Vector Cross Product

Enter the X, Y and Z components of two vectors to find their cross product instantly. The calculator shows the resulting vector, its magnitude and the full step-by-step calculation.