Geometry Calculator - Mongolian Numerals
Calculate area, volume, perimeter, and surface area for circles, triangles, rectangles, spheres, and more geometric shapes with Mongolian numeral system support.
About This Numeral System
Mongolian numerals (᠐ through ᠙) are the digits of the traditional Mongolian script, a vertical script written top-to-bottom and left-to-right in columns. This script is used primarily in the Inner Mongolia Autonomous Region of China, where it remains an official script alongside Chinese. In the independent country of Mongolia (Outer Mongolia), the traditional script was replaced by Cyrillic in the 1940s, though there has been a gradual revival movement in recent years. This calculator displays results in traditional Mongolian numerals for users who read and write in the traditional Mongolian script.
A free online geometry calculator for 2D and 3D shapes. Calculate area and perimeter for circles, triangles, rectangles, squares, parallelograms, trapezoids, pentagons, hexagons, and ellipses. Calculate volume and surface area for spheres, cubes, rectangular prisms, cylinders, cones, and pyramids. The calculator can also solve for a missing dimension when you know the area or volume — for example, find the radius of a circle given its area. Each result includes the formula used, the substitution of values, and step-by-step intermediate calculations, making it a learning tool as well as a calculator.
How This Calculator Works
Geometry Formulas: Circle: A = πr², P = 2πr | Triangle: A = ½ × b × h | Sphere: V = 4/3 πr³
Each shape uses its standard formula. The calculator substitutes the input values into the formula and shows each intermediate step. For solving unknown dimensions, the formula is rearranged algebraically — for example, given the area of a circle, the radius is computed as r = √(A / π).
Frequently Asked Questions
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.
Does Mongolia (the country) still use these traditional numerals?
Not in daily life. The independent country of Mongolia switched to Cyrillic script in the 1940s and uses Western Arabic numerals (0–9) for numbers. The traditional Mongolian numerals on this calculator are primarily relevant for users in Inner Mongolia (China), where the vertical script remains official, and for scholars working with historical Mongolian documents.
Worked Examples
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.
Key Features
- 10 two-dimensional shapes
- 6 three-dimensional shapes
- Solve for unknown dimensions
- Detailed step-by-step working
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