Area Calculator – Calculate Area of Rectangles, Triangles, Circles, Trapezoids & 3 More Shapes

  • Adam
  • November 4, 2025

Free online area calculator for 7 shapes: rectangles, triangles, circles, trapezoids, sectors, ellipses, and parallelograms. Instant results with step-by-step formulas and unit conversions.

Area Calculator

Calculate Area for 7 Common Shapes with Complete Formulas and Step-by-Step Solutions

Quick Navigation

Area Calculators for Common Shapes

Select your shape and enter dimensions. Results display instantly with formulas.

Rectangle Area
Area
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Triangle Area (Heron's Formula)
Area
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Trapezoid Area
Area
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Circle Area
Area
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Sector Area
Area
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Ellipse Area
Area
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Parallelogram Area
Area
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Understanding Area

Area measures the amount of two-dimensional space an object occupies. Expressed in square units (m², ft², cm², etc.), area differs from perimeter which measures distance around an object. The SI unit for area is the square meter (m²), though practical applications use various units depending on context.

Area calculations are fundamental across mathematics, science, architecture, engineering, and surveying. From designing building layouts to planning agricultural land use, understanding how to calculate area is essential. Different shapes require different formulas based on their geometric properties. Some formulas use base and height; others use radius or lengths of sides.

Complex irregular shapes can be approximated by dividing them into simpler geometric components and summing their areas. This principle applies universally from land surveying to material estimation in construction projects.

Key Principle: Area is always measured in square units. When multiplying dimensions, track units carefully: meters × meters = square meters (m²).

Key Features & Capabilities

7 Shapes Rectangle, triangle, trapezoid, circle, sector, ellipse, parallelogram
Multiple Units Meters, feet, inches, centimeters supported
Instant Results Calculate areas in real-time with precision
Clear Formulas Each shape displays exact formula used
Step-by-Step Detailed calculation breakdown provided
Mobile Optimized Fully responsive on all devices

How to Use This Calculator

General Instructions

  1. Select Your Shape: Choose which geometric shape matches your object
  2. Measure Dimensions: Carefully measure all required dimensions (length, width, radius, height, etc.)
  3. Choose Unit: Select your measurement unit from dropdown menu
  4. Enter Values: Input all measurements into form fields
  5. Click Calculate: Press Calculate button to compute area
  6. Review Results: See area with step-by-step calculation shown

Tips for Accurate Calculations

  • Consistent Units: All measurements must use the same unit system
  • Height vs Side: "Height" must be perpendicular distance between parallel sides, not a slant edge
  • Radius vs Diameter: For circles, use radius (r = d/2). Don't use diameter directly
  • Triangle Validity: Ensure three sides can form a valid triangle. Sum of any two sides must exceed the third
  • Precision Matters: More precise measurements yield more accurate area calculations

Complete Formulas Reference

Rectangle
Area = l × w
Where l = length, w = width
Triangle (Heron's Formula)
Area = √(s(s-a)(s-b)(s-c))
Where s = (a+b+c)/2 (semiperimeter)
a, b, c are the three sides
Trapezoid
Area = ((b₁ + b₂) / 2) × h
Where b₁, b₂ are parallel bases
h = perpendicular height
Circle
Area = π × r²
Where r = radius
Sector
Area = (θ/360°) × π × r² [degrees]
Area = (θ/2π) × π × r² = (θ × r²)/2 [radians]
Where θ = central angle, r = radius
Ellipse
Area = π × a × b
Where a = semi-major axis
b = semi-minor axis
Parallelogram
Area = b × h
Where b = base
h = perpendicular height (not side length)

Shape Reference Guide

Rectangle

Four-sided shape with four right angles. Opposite sides equal length. Simplest shape for area calculation. Formula: Area = length × width.

Triangle

Three-sided polygon. Heron's formula works for any triangle given three sides: Area = √(s(s-a)(s-b)(s-c)). Alternative: Area = ½ × base × height.

Trapezoid

Quadrilateral with one pair of parallel sides (bases). Height measured perpendicular between bases. Formula: Area = ((b₁ + b₂) / 2) × h.

Circle

Set of all points equidistant from center. Defined by radius or diameter. Formula: Area = π × r². Perfect circle no edges or corners.

Sector

Portion of circle enclosed by two radii and an arc. Think of pizza slice. Central angle determines size. Formula varies by angle units (degrees vs radians).

Ellipse

Oval shape with two different radii (semi-major and semi-minor axes). Circle is special case where both radii equal. Formula: Area = π × a × b.

Parallelogram

Quadrilateral with opposite sides parallel and equal. Unlike rectangle, corners aren't necessarily 90°. Height perpendicular to base. Formula: Area = b × h.

Area Unit Conversions

Convert between different area measurement systems using these relationships:

UnitSquare Meters (m²)Square Feet (ft²)Square Inches (in²)Hectares
1 Square Meter110.7641,5500.0001
1 Square Foot0.092911440.0000093
1 Square Inch0.006450.0069410.0000006
1 Hectare10,000107,64015,500,0001
1 Square Kilometer1,000,00010,764,0001,550,000,000100

Worked Examples

Example 1: Rectangle Area - Land Plot

Problem: Rectangular property: length 220 feet, width 99 feet. Find area in square feet.

Solution:
Area = l × w = 220 × 99 = 21,780 ft²
This equals approximately 0.5 acres (1 acre = 43,560 ft²)

Example 2: Triangle Area - Pool (Heron's Formula)

Problem: Triangular pool with sides 77 ft, 77 ft, 77 ft. Find area in sq ft.

Solution:
s = (77 + 77 + 77) / 2 = 115.5
Area = √(115.5 × 38.5 × 38.5 × 38.5) = √2,567,333 ≈ 2,567.33 ft²

Example 3: Circle Area - Crop Circle

Problem: Circular crop circle with radius 15 ft. Find area.

Solution:
Area = π × r² = π × 15² = π × 225 ≈ 706.858 ft²

Example 4: Sector Area - Pie Slice

Problem: Pie with radius 16 inches. Find area of 60° sector (1/6 of pie).

Solution:
Area = (60°/360°) × π × r²
Area = (1/6) × π × 16²
Area = (1/6) × π × 256 ≈ 134.041 in²
Each person gets 1/3 less pie (area-wise)

Example 5: Parallelogram Area - Ramp

Problem: Parallelogram ramp with base 29.528 ft, height 9 ft. Find area.

Solution:
Area = b × h = 29.528 × 9 = 265.752 sq ft
Area can hold ramp with approximately double the area of Olympic pool

Frequently Asked Questions

❓ What's the difference between area and perimeter?
Area measures interior 2D space (square units). Perimeter measures distance around boundary (linear units). Both important but measure different things.
❓ Why use "height" instead of "side" for parallelograms?
Height must be perpendicular to base. A slant side is longer but doesn't determine area. Only perpendicular distance matters for area calculation.
❓ Can I use Heron's formula for any triangle?
Yes. Heron's formula works for any triangle when you know all three sides. No need for height or angles. Most general triangle area formula.
❓ What's the relationship between circle and sector?
Sector is fraction of circle. If angle is 90°, sector is ¼ of full circle. Full circle = 360°. Angle determines what fraction of circle the sector represents.
❓ How are ellipse and circle related?
Circle is special ellipse where both semi-axes equal. Circle: a = b, so Area = π × r². Ellipse: a ≠ b, so Area = π × a × b (more general formula).
❓ What if triangle sides can't form valid triangle?
Triangle inequality: sum of any two sides must exceed third side. If not satisfied, points don't form closed triangle. Calculator will indicate invalid input.

Calculate Area Instantly

Whether you're planning construction, designing landscapes, calculating land area, or solving geometry problems, this comprehensive area calculator handles 7 common shapes with instant results and complete step-by-step analysis. Fast, accurate, completely free.

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