Square Footage Calculator: Area of Shapes & Rooms

Q: What is the formula for a ring's area?

The area of a ring (annulus) is calculated as π × (R² - r²), where R is the outer radius and r is the inner radius. This formula finds the area of the outer circle and subtracts the area of the inner circle, giving you the ring's area.

Q: How do I calculate square footage from three sides of a triangle?

Use Heron's formula: First calculate the semi-perimeter s = (a + b + c) / 2, then the area is √[s(s-a)(s-b)(s-c)]. Our calculator automatically validates that your three sides form a valid triangle (the sum of any two sides must be greater than the third).

Q: What is the difference between area and surface area?

Area measures the flat surface of a 2D shape (like a floor or wall). Surface area measures the total area of all faces of a 3D object (like a box or sphere). This calculator finds 2D area. For 3D objects, you'd need to calculate each face separately and sum them.

Q: How do I calculate the area of a sector?

A sector (pie slice) area is calculated as (θ/360) × πr², where θ is the angle in degrees and r is the radius. The arc length (curved edge) is (θ/360) × 2πr. Our calculator shows both area and arc length for sectors.

Q: What is the formula for a parallelogram area?

Parallelogram area is A = b × h, where b is the base length and h is the perpendicular height. This differs from a rectangle because the height is measured perpendicular to the base, not along the slanted side. The formula is the same as a rectangle because a parallelogram can be rearranged into a rectangle.

Square Footage Calculator: Unified Geometry & Spatial Intelligence

Calculate area and perimeter for 9 geometric shapes with real-time updates. Switch between units seamlessly with automatic conversions.

Geometry Insights

Shape Library

•Nine specialized shapes from basic rectangles to advanced sectors and rings.

•Each shape uses optimized formulas for precision, with real-time validation for complex shapes like Heron's triangle.

Unit Synchronization

•Change the global unit and all inputs convert instantly.

•No manual recalculation needed—switch between feet, meters, or any unit seamlessly.

Perimeter & Arc Length

•Essential for trim, fencing, and edging calculations.

•Every shape includes perimeter/circumference, with special metrics like arc length for sectors.

Visual Dimension Guides

•Each shape displays a diagram with labeled dimensions.

•Clear visual indicators show exactly which measurements correspond to each input field.

Square Footage Calculator: Area of Rectangle, Circle, Triangle & More

Free square footage calculator for 9 geometric shapes. Calculate area, perimeter, and arc length. Supports feet, meters, and all common units with instant conversions.

Advanced Geometry Guide

Understanding Area vs. Surface Area

Area (2D):

Measures the flat surface of a shape. Used for flooring, paint coverage, carpet, and landscaping. Examples: room floor (rectangle), circular patio (circle), triangular garden bed (triangle).
Surface Area (3D):

Measures the total area of all faces of a 3D object. Used for wrapping paper, paint on boxes, or material needed to cover a 3D shape. Requires calculating each face separately.
When to Use Each:

Use area for flat surfaces (floors, walls, yards). Use surface area for 3D objects (boxes, spheres, cylinders). This calculator focuses on 2D area calculations.

Area measures flat 2D surfaces, while surface area measures all faces of 3D objects.

Formula Cheat Sheet

Rectangle:

A = L × W
where L is length and W is width.
Rectangle Border (Hollow):

A = (L_outer × W_outer) - (L_inner × W_inner)
Outer rectangle area minus inner rectangle area.
Parallelogram:

A = b × h
where b is base and h is perpendicular height. Same as rectangle because a parallelogram can be rearranged into a rectangle.
Trapezoid:

A = ¹⁄₂(a + b) × h
where a and b are the two parallel bases, and h is the height.
Circle:

A = π × r²
where r is the radius. Circumference: C = 2πr.
Ring (Annulus):

A = π × (R² - r²)
where R is outer radius and r is inner radius. Outer circle area minus inner circle area.
Sector (Pie Slice):

A = (θ / 360) × πr²
where θ is the angle in degrees and r is the radius. Arc length: L = (θ / 360) × 2πr.
Triangle (Base/Height):

A = ¹⁄₂ × b × h
where b is base and h is perpendicular height.
Triangle (Heron's Formula):

s = (a + b + c) / 2
A = √[s(s - a)(s - b)(s - c)]
where s is the semi-perimeter and a, b, c are the three side lengths. Requires triangle inequality: sum of any two sides > third side.

Quick reference for all formulas used in this calculator.

Practical Applications

Real-World Use Cases

Flooring & Carpet:

Calculate exact square footage needed for flooring materials. Account for waste by adding 5-10% to your total area for cuts and pattern matching.
Paint Coverage:

Determine wall area for paint estimates. Most paints cover 350-400 sq ft per gallon, but check manufacturer specifications for your chosen product.
Landscaping:

Plan garden beds, patios, and walkways. Use circle and sector shapes for curved designs, and combine multiple shapes for complex layouts.
Material Ordering:

Convert between square feet, square yards, and square meters to match supplier units. Many materials are sold by square yards (carpet) or square meters (tiles).

Square footage calculations are essential for many home improvement and construction projects.

FAQ

? How do I calculate the area of an L-shaped room?

For L-shaped rooms, break the space into two rectangles. Calculate the area of each rectangle separately, then add them together. For example, if one rectangle is 10 ft × 8 ft (80 sq ft) and the other is 6 ft × 4 ft (24 sq ft), the total area is 104 sq ft.

? What is the formula for a ring's area?

The area of a ring (annulus) is calculated as π × (R² - r²), where R is the outer radius and r is the inner radius. This formula finds the area of the outer circle and subtracts the area of the inner circle, giving you the ring's area.

? How do I calculate square footage from three sides of a triangle?

Use Heron's formula: First calculate the semi-perimeter s = (a + b + c) / 2, then the area is √[s(s-a)(s-b)(s-c)]. Our calculator automatically validates that your three sides form a valid triangle (the sum of any two sides must be greater than the third).

? What is the difference between area and surface area?

Area measures the flat surface of a 2D shape (like a floor or wall). Surface area measures the total area of all faces of a 3D object (like a box or sphere). This calculator finds 2D area. For 3D objects, you'd need to calculate each face separately and sum them.

? How do I calculate the area of a sector?

A sector (pie slice) area is calculated as (θ/360) × πr², where θ is the angle in degrees and r is the radius. The arc length (curved edge) is (θ/360) × 2πr. Our calculator shows both area and arc length for sectors.

? What is the formula for a parallelogram area?

Parallelogram area is A = b × h, where b is the base length and h is the perpendicular height. This differs from a rectangle because the height is measured perpendicular to the base, not along the slanted side. The formula is the same as a rectangle because a parallelogram can be rearranged into a rectangle.

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