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Geometry Formula Sheet

The most-used geometry formulas for middle school, high school and college prep. Each formula includes a worked example with its US customary → metric conversion, so you can check both the math and the unit conversion in one place.

Rectangle area

sq units (e.g. sq ft, m²)

A = l × w

Example: A 4 ft × 6 ft tabletop: A = 4 × 6 = 24 sq ft = 2.23 m²

l = length, w = width

Rectangle perimeter

units (e.g. ft, m)

P = 2(l + w)

Example: A 4 ft × 6 ft table: P = 2(4 + 6) = 20 ft = 6.10 m

Triangle area

sq units

A = ½ × b × h

Example: Base 10 in, height 6 in: A = ½ × 10 × 6 = 30 sq in = 193.5 cm²

b = base, h = height

Circle area

sq units

A = π × r²

Example: Radius 5 cm: A = π × 25 ≈ 78.5 cm² ≈ 12.2 sq in

π ≈ 3.14159

Circle circumference

units

C = 2 × π × r

Example: Radius 5 cm: C = 2 × π × 5 ≈ 31.4 cm ≈ 12.4 in

Trapezoid area

sq units

A = ½ × (a + b) × h

Example: Bases 6 and 10 ft, height 4 ft: A = ½ × 16 × 4 = 32 sq ft ≈ 2.97 m²

a, b = parallel bases, h = height

Cube volume

cubic units (e.g. cu ft, m³)

V = s³

Example: Side 3 ft: V = 27 cu ft ≈ 0.765 m³

Rectangular prism volume

cubic units

V = l × w × h

Example: 8 × 5 × 4 ft: V = 160 cu ft ≈ 4.53 m³

Cylinder volume

cubic units

V = π × r² × h

Example: Radius 2 ft, height 10 ft: V ≈ 125.7 cu ft ≈ 3.56 m³

Sphere volume

cubic units

V = ⁴⁄₃ × π × r³

Example: Radius 3 in: V ≈ 113.1 cu in ≈ 0.065 cu ft

Cone volume

cubic units

V = ⅓ × π × r² × h

Example: Radius 2 ft, height 6 ft: V ≈ 25.1 cu ft ≈ 0.71 m³

Pythagorean theorem

any consistent unit

a² + b² = c²

Example: Legs 3 and 4: c = √(9 + 16) = 5 units

Right triangle only

Practice the conversion too

These examples convert US customary to metric using the exact NIST / SI constants. Open a converter to check any value:

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Frequently Asked Questions

Why do area answers need squared units?

Area measures two dimensions, so units are squared (sq ft, m², sq in, cm²). Multiplying feet × feet gives square feet. Volume measures three dimensions and uses cubed units (cu ft, m³).

Is π exact?

π is an irrational number with infinite decimals. For schoolwork, 3.14 or 3.1416 is standard; for exact answers, leave π in the result (e.g. 25π sq cm).

How do I convert sq ft to sq m?

Multiply by the exact constant 0.09290304 (1 sq ft = 0.09290304 m²). Converting lengths first then squaring gives the same result.

When do I use ½ × b × h instead of l × w?

Use ½ × b × h for triangles (a triangle is half a rectangle with the same base and height). Use l × w for rectangles.

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Last Updated 2026 | Formulas are standard textbook content; conversion constants trace to NIST SP 330 & the BIPM SI Brochure.