From triangles to spheres — calculate area, perimeter, volume, and missing dimensions for every standard geometric shape. Step-by-step solutions with AI explanations.
Whatever shape you are working with — a 2D triangle for a homework problem or a 3D sphere for an engineering spec — this page sends you to the right tool. Each calculator below accepts the dimensions you have, infers the ones you do not, and returns area, perimeter, volume, surface area, and any other derived quantity that matches the shape. Numerical results are instant; for full step-by-step reasoning with AI explanations, use the AI Solve button on any tool.
A "shape calculator" is shorthand for a whole family of geometry tools. Below we group them into two sections — 2D figures (flat shapes, work in area and perimeter) and 3D solids (work in volume and surface area) — and link to each dedicated solver. If you have a compound figure (an L-shape, a stadium, a window with an arched top), use the Composite Figure Calculator at the bottom of the 2D section: it accepts a textual or photographic description and returns the total measurements.
Quick lookup for the formulas the calculators apply behind the scenes. All formulas use SI-style notation (no specific units) so they work for centimetres, metres, inches, or any consistent unit you choose.
| Shape | Area | Perimeter |
|---|---|---|
| Triangle | ½ × b × h · Heron: √(s(s−a)(s−b)(s−c)) | a + b + c |
| Square | s² | 4s |
| Rectangle | l × w | 2(l + w) |
| Parallelogram | b × h | 2(a + b) |
| Trapezoid | ½ × (b₁ + b₂) × h | b₁ + b₂ + a + c |
| Rhombus | ½ × d₁ × d₂ | 4s |
| Kite | ½ × d₁ × d₂ | 2(a + b) |
| Circle | π × r² | 2π × r (circumference) |
| Regular polygon (n-gon) | ½ × n × s × apothem | n × s |
| Sector of circle | ½ × r² × θ (θ in radians) | 2r + r × θ |
| Solid | Volume | Surface area |
|---|---|---|
| Cube | s³ | 6s² |
| Rectangular prism (box) | l × w × h | 2(lw + lh + wh) |
| Sphere | (4/3) × π × r³ | 4π × r² |
| Cylinder | π × r² × h | 2π × r² + 2π × r × h |
| Cone | (1/3) × π × r² × h | π × r × (r + slant) |
| Square pyramid | (1/3) × a² × h | a² + 2 × a × slant |
| Triangular prism | base area × length | 2 × base area + (perimeter × length) |
| Hemisphere | (2/3) × π × r³ | 3π × r² |
2D shapes are flat figures lying in a single plane — you measure their area (square units) and perimeter (linear units). 3D shapes have depth, so they are measured by volume (cubic units), surface area (square units), and sometimes lateral or face area. A 2D shape calculator returns area and perimeter; a 3D shape calculator returns volume and surface area as well.
Yes — most calculators on this site work backward as well as forward. If you know a circle's area, the calculator returns the radius, diameter and circumference. If you know a triangle's three sides, it returns the angles. Look at each calculator's input form: optional fields can be left blank and the tool infers them from the values you provide.
Yes — every calculator is free to use, with no signup required for numerical results. AI Solve (full step-by-step reasoning) uses 3 credits per request; new accounts receive 30 free credits, enough for 10 AI solutions. The calculators themselves never expire and have no usage cap.
Yes — use the Composite Figure Calculator listed above. Describe the figure as a list of sub-shapes (e.g. "rectangle 10×6 plus triangle base 6 height 4 on top") or upload a photo, and the AI returns the total area and perimeter, including subtracting any cut-outs.
Yes. For irregular polygons defined by their vertices, use the Quadrilateral with Points Calculator (4 vertices) or the Composite Figure Calculator (any number of vertices). For polygons defined by sides and angles, use the regular polygon tools and adjust manually.
Calculations use standard double-precision floating-point arithmetic and are rounded to 4 decimal places by default (configurable in your account settings). For most homework, engineering and design contexts this is well beyond the precision of the input measurements. For results that must be exact (proofs, symbolic geometry), use the AI Solve feature, which preserves exact form (e.g. √2, π) instead of decimal approximations.
Browse all 70+ calculators by topic, or jump to the 3D-only guide for solids.