Geometry Calculator - Lepcha Numerals

Input: Circle with radius 5 cm

Result: Area = π × 5² = 78.54 cm². Perimeter = 2π × 5 = 31.42 cm.

Input: Rectangle 6 m × 4 m

Result: Area = 6 × 4 = 24 m². Perimeter = 2(6 + 4) = 20 m.

How do I find the area of an irregular shape?

For irregular shapes, break them into regular shapes you can calculate. For an L-shaped room, split it into two rectangles, calculate each area, and add them. For a circular segment combined with a rectangle, calculate each part separately. The calculator supports all the common shapes you need for this decomposition approach.

What is the difference between surface area and lateral area?

Lateral area is the area of only the sides of a 3D shape — not including the base or top. Surface area includes all faces: the sides plus the base and top. For a cylinder, lateral area is 2πrh (the curved side only), while total surface area is 2πrh + 2πr² (the side plus both circular ends). The calculator shows both values where applicable.

How does the calculator handle the volume of a truncated cone?

Select the 3D category and choose "Cone" or the frustum option if available. Enter the top radius, bottom radius, and height. The calculator uses the formula V = (1/3)πh(R² + Rr + r²), where R and r are the two radii. This is useful for calculating the volume of buckets, planters, and architectural elements.

What can the geometry calculator do?

The geometry calculator supports 2D shapes (circle, triangle, rectangle, square, parallelogram, trapezoid, pentagon, hexagon, ellipse) and 3D shapes (sphere, cube, rectangular prism, cylinder, cone, pyramid). For 2D shapes it calculates area and perimeter. For 3D shapes it calculates volume and surface area. It can also solve for a missing dimension when given the area or volume.

How do I use the pyramid geometry calculator?

Select the 3D category and choose "Pyramid". Enter the base dimensions and height (or slant height, depending on what you know). The calculator computes the volume using V = (1/3) × base_area × height and the surface area including all triangular faces. For a square pyramid with base side 4 and height 6, the volume is (1/3) × 16 × 6 = 32 cubic units.

How does the solution steps feature work?

Click the "Show Solution" button after calculating to see step-by-step work. This includes the formula used, substitution of values, intermediate calculations, and the final answer. This is perfect for learning how geometry formulas work and verifying calculations.

Is this an online geometry calculator?

Yes. This is a free online geometry calculator that runs entirely in your browser with no download or sign-up. It supports both 2D and 3D shapes, shows step-by-step solutions, and can solve for missing dimensions. All calculations happen locally on your device.

Why do Lepcha letters look rotated compared to Tibetan?

The Lepcha script was originally written vertically, like its Tibetan ancestor. When it was adapted for horizontal writing, the letterforms were effectively rotated 90 degrees — what was originally a top-to-bottom stroke became a left-to-right stroke. This rotation gives Lepcha its distinctive appearance, where letters that look familiar to Tibetan readers appear sideways or upside-down. The numerals inherited this rotation.