Calculator.

Geometry Calculator.

Calculate area, perimeter, volume, and surface area for 2D and 3D shapes. Perfect for students, engineers, and real-world applications.

cm

Enter dimensions to see visualization

What is Geometry?

Geometry is the branch of mathematics that studies the properties, measurements, and relationships of points, lines, angles, surfaces, and solids. The word comes from the Greek words "geo" (earth) and "metron" (measurement).

How to Use This Calculator

  1. Choose between 2D (flat) or 3D (solid) shapes
  2. Select the specific shape you want to calculate
  3. Choose your preferred unit of measurement
  4. Enter the required dimensions
  5. View instant results including area, perimeter, volume, and more

2D Shapes (Plane Geometry)

Two-dimensional shapes have length and width but no depth. They exist on a flat plane.

  • Circle, Ellipse, Sector

  • Rectangle, Square, Parallelogram

  • Triangle, Trapezoid, Regular Polygon

3D Shapes (Solid Geometry)

Three-dimensional shapes have length, width, and height. They occupy space and have volume.

  • Sphere (ball shape)

  • Cube, Cuboid (box shapes)

  • Cylinder, Cone, Pyramid

Real-World Applications

Construction & Architecture

Calculate flooring area, wall paint coverage, room volumes for HVAC, roof slopes

Engineering & Design

Tank volumes, pipe dimensions, material requirements, structural calculations

Education & Learning

Homework help, exam preparation, understanding geometric concepts visually

Landscaping & Gardening

Garden bed areas, mulch volumes, pond sizes, fence perimeters

Manufacturing

Material cutting, container volumes, packaging dimensions

Home Improvement

Tile calculations, carpet area, concrete for driveways

Geometry Formulas Reference

2D Shape Formulas

Circle

A=πr2A = \pi r^2
C=2πrC = 2\pi r

r = radius

Rectangle

A=l×wA = l \times w
P=2(l+w)P = 2(l + w)
d=l2+w2d = \sqrt{l^2 + w^2}

l = length, w = width, d = diagonal

Square

A=s2A = s^2
P=4sP = 4s
d=s2d = s\sqrt{2}

s = side length, d = diagonal

Triangle (Heron's Formula)

s=a+b+c2s = \frac{a+b+c}{2}
A=s(s−a)(s−b)(s−c)A = \sqrt{s(s-a)(s-b)(s-c)}

a, b, c = sides, s = semi-perimeter

Trapezoid

A=(b1+b2)2×hA = \frac{(b_1 + b_2)}{2} \times h

b₁, b₂ = parallel bases, h = height

Ellipse

A=πabA = \pi a b
P≈π(a+b)P \approx \pi(a+b)

a = semi-major axis, b = semi-minor axis

Sector

A=θ360×πr2A = \frac{\theta}{360} \times \pi r^2
L=θ360×2πrL = \frac{\theta}{360} \times 2\pi r

θ = angle in degrees, r = radius, L = arc length

Regular Polygon

A=ns24tan⁡(π/n)A = \frac{ns^2}{4\tan(\pi/n)}
P=n×sP = n \times s

n = number of sides, s = side length

Parallelogram

A=b×hA = b \times h
P=2(a+b)P = 2(a + b)

b = base, h = height, a = side

3D Shape Formulas

Sphere

V=43πr3V = \frac{4}{3}\pi r^3
SA=4πr2SA = 4\pi r^2

r = radius, V = volume, SA = surface area

Cube

V=s3V = s^3
SA=6s2SA = 6s^2
d=s3d = s\sqrt{3}

s = side, d = space diagonal

Cuboid (Rectangular Prism)

V=l×w×hV = l \times w \times h
SA=2(lw+wh+hl)SA = 2(lw + wh + hl)

l = length, w = width, h = height

Cylinder

V=πr2hV = \pi r^2 h
SA=2πr(r+h)SA = 2\pi r(r + h)
LSA=2πrhLSA = 2\pi r h

r = radius, h = height, LSA = lateral surface area

Cone

V=13πr2hV = \frac{1}{3}\pi r^2 h
l=r2+h2l = \sqrt{r^2 + h^2}
SA=πr(r+l)SA = \pi r(r + l)

r = radius, h = height, l = slant height

Pyramid (Rectangular Base)

V=13×B×hV = \frac{1}{3} \times B \times h
B=l×wB = l \times w

B = base area, h = height, l = length, w = width

Key Mathematical Constants

π (Pi) ≈ 3.14159

Ratio of circumference to diameter

√2 ≈ 1.41421

Diagonal of unit square

√3 ≈ 1.73205

Space diagonal factor for cube

Frequently Asked Questions

“Percentages help us measure change, compare values, and make better decisions — one simple symbol with endless meaning.”

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