Geometry Solver
Enter any known variables (radius, area, etc.) and instantly solve for the rest.
Also Try Scientific Calculator →1. Select a Shape
2. Enter Known Variables
The Complete Guide to Euclidean Geometry, 2D Plane Shapes & 3D Solid Spatial Formulas
Solving spatial geometry problems manually requires manipulating multi-variable algebraic equations, converting between radians and degrees, and applying Euclidean theorems. A missing square root, inverted trigonometric ratio (sin, cos, tan), or misplaced π factor can compromise engineering blueprints, architectural estimates, or physics homework assignments.
The s0lve.it Interactive Geometry Solver dynamically solves 14 planar 2D polygons and 3D spatial solids. With bidirectional equation solving (enter any subset of known variables to solve all remaining dimensions) and interactive SVG diagrams with real-time visual highlight states, all calculations execute 100% locally in your browser's RAM with zero server latency.
Geometric Formulas Reference: 2D Polygons & 3D Solids
| Geometric Shape | Spatial Type | Area / Surface Area Formula | Perimeter / Volume Formula |
|---|---|---|---|
| Circle | 2D Plane | A = π · r² | C = 2πr = πd |
| Right Triangle | 2D Plane | A = ½ · a · b | P = a + b + √(a² + b²) |
| Trapezoid | 2D Plane | A = ((a + b) / 2) · h | P = a + b + c + d |
| Sphere | 3D Solid | A = 4πr² | V = (4/3) · π · r³ |
| Cylinder | 3D Solid | A = 2πr(r + h) | V = π · r² · h |
| Cone | 3D Solid | A = πr(r + √(h² + r²)) | V = ⅓ · π · r² · h |
| Torus (Donut) | 3D Solid | A = 4π² · R · r | V = 2π² · R · r² |
Interactive Bidirectional Equation Solving
Unlike standard calculators that require forward dimension inputs, this solver features bidirectional algebraic solving. If you know the volume and radius of a cylinder, entering them immediately computes the required height, lateral surface area, and base diameter without manual algebraic manipulation.
Frequently Asked Questions (FAQ)
What is an interactive geometry solver and shape calculator?
An interactive geometry solver calculates missing properties of 2D polygons and 3D solids from any subset of known inputs. It combines mathematical formulas with real-time vector diagram highlights.
How do I calculate the hypotenuse and angles of a right triangle?
Enter any two side lengths or one side and an acute angle. The engine applies the Pythagorean theorem (a² + b² = c²) and inverse trigonometric functions (arcsin, arccos, arctan) to calculate all three sides, angles, perimeter, and area.
How is the volume and surface area of a 3D sphere or cylinder computed?
The solver applies exact Euclidean volume equations: V = (4/3) · π · r³ for spheres and V = π · r² · h for cylinders, outputting both volume and total surface area with decimal precision.
Can I calculate trapezoids with non-equal legs (scalene trapezoids)?
Yes. The solver supports isosceles, right, and general scalene trapezoids, calculating base projections, individual leg lengths, interior angles, perimeter, and total enclosed area.
What happens when I hover over an input field?
Hovering or focusing on any input variable dynamically highlights that specific dimension (e.g. radius r, slant height l, or angle α) directly on the interactive SVG diagram in glowing accent blue.
Are my engineering calculations or homework entries stored on remote servers?
No. All geometric calculations and trigonometric evaluations execute 100% locally in your browser's private memory. Zero dimensions or formulas are ever sent to the cloud.
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