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Math Formula Sheet: 41 Formulas, Each With a Worked Example

On GED sheet 33 the official GED sheet gives youLearn it 8 it leaves out

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Area

Square
On GED sheet
A = s²
Example: s = 6 in: A = 6² = 36 sq in
Rectangle
On GED sheet
A = lw
Example: 12 ft by 9 ft: A = 12 × 9 = 108 sq ft
Parallelogram
On GED sheet
A = bh
Example: b = 10 cm, h = 4 cm: A = 10 × 4 = 40 sq cm
Lesson: Area of a parallelogram →
Triangle
On GED sheet
A = 12bh
Example: b = 8 m, h = 5 m: A = ½ × 8 × 5 = 20 sq m
Trapezoid
On GED sheet
A = 12h(b₁ + b₂)
Example: b₁ = 6 ft, b₂ = 10 ft, h = 4 ft: A = ½ × 4 × (6 + 10) = 2 × 16 = 32 sq ft
Lesson: Area of a trapezoid →
Circle
On GED sheet
A = πr²
Example: r = 3 in: A ≈ 3.14 × 3² = 3.14 × 9 = 28.26 sq in

Perimeter and circumference

Square
On GED sheet
P = 4s
Example: s = 9 ft: P = 4 × 9 = 36 ft
Rectangle
On GED sheet
P = 2l + 2w
Example: 15 yd by 8 yd: P = 2(15) + 2(8) = 30 + 16 = 46 yd
Triangle
On GED sheet
P = s₁ + s₂ + s₃
Example: sides 5, 7 and 9 cm: P = 5 + 7 + 9 = 21 cm
Circle (circumference)
On GED sheet
C = 2πr or C = πd
Example: d = 20 in: C ≈ 3.14 × 20 = 62.8 in

Volume

Rectangular prism (box)
On GED sheet
V = lwh
Example: l = 10, w = 4, h = 3 in: V = 10 × 4 × 3 = 120 cu in
Right prism
On GED sheet
V = Bh
Example: B = 15 sq cm, h = 6 cm: V = 15 × 6 = 90 cu cm
Cylinder
On GED sheet
V = πr²h
Example: r = 2 ft, h = 5 ft: V ≈ 3.14 × 2² × 5 = 62.8 cu ft
Lesson: Volume of a cylinder →
Pyramid
On GED sheet
V = 13Bh
Example: B = 36 sq m, h = 5 m: V = (36 × 5) ÷ 3 = 60 cu m
Cone
On GED sheet
V = 13πr²h
Example: r = 3 cm, h = 4 cm: V ≈ (3.14 × 3² × 4) ÷ 3 = 113.04 ÷ 3 = 37.68 cu cm
Sphere
On GED sheet
V = 43πr³
Example: r = 3 in: V ≈ (4 × 3.14 × 3³) ÷ 3 = 339.12 ÷ 3 = 113.04 cu in

Surface area

Rectangular prism (box)
On GED sheet
SA = 2lw + 2lh + 2wh
Example: a 5 × 4 × 2 box: SA = 2(20) + 2(10) + 2(8) = 76 sq units
Right prism
On GED sheet
SA = ph + 2B
Example: p = 12, h = 10, B = 6: SA = 12 × 10 + 2 × 6 = 132 sq units
Cylinder
On GED sheet
SA = 2πrh + 2πr²
Example: r = 2, h = 5: SA ≈ 62.8 + 25.12 = 87.92 sq units
Pyramid
On GED sheet
SA = 12ps + B
Example: 6 by 6 base, s = 5: SA = ½ × 24 × 5 + 36 = 96 sq units
Cone
On GED sheet
SA = πrs + πr²
Example: r = 3, s = 5: SA ≈ 47.1 + 28.26 = 75.36 sq units
Sphere
On GED sheet
SA = 4πr²
Example: r = 2: SA ≈ 4 × 3.14 × 2² = 50.24 sq units

Right triangles

Pythagorean theorem
On GED sheet
a² + b² = c²
Example: legs 5 and 12: c² = 25 + 144 = 169, so c = √169 = 13

Lines and graphs

Slope
On GED sheet
m = y₂ − y₁x₂ − x₁
Example: (1, 2) and (4, 11): m = (11 − 2) ÷ (4 − 1) = 9 ÷ 3 = 3
Lesson: Slope of a line →
Slope-intercept form
On GED sheet
y = mx + b
Example: $45 a month plus $6 a gig: y = 6x + 45; 3 gigs: y = 6(3) + 45 = $63
Point-slope form
On GED sheet
y − y₁ = m(x − x₁)
Example: slope 2 through (3, 5): y − 5 = 2(x − 3), so y = 2x − 1
Lesson: Point-slope form →
Distance between two points
Learn it
d = √((x₂ − x₁)² + (y₂ − y₁)²)
Example: (1, 2) and (4, 6): d = √(3² + 4²) = √25 = 5
Midpoint
Learn it
M = (x₁ + x₂2, y₁ + y₂2)
Example: (2, 3) and (8, 7): M = (10 ÷ 2, 10 ÷ 2) = (5, 5)

Quadratics

Standard form
On GED sheet
y = ax² + bx + c
Example: y = 2x² − 3x + 1: a = 2, b = −3, c = 1
Quadratic formula
On GED sheet
x = −b ± √(b² − 4ac)2a
Example: x² + 2x − 8 = 0: x = (−2 ± √36) ÷ 2 = (−2 ± 6) ÷ 2, so x = 2 or x = −4

Money, percents and rates

Simple interest
On GED sheet
I = Prt
Example: $500 at 4% for 3 years: I = 500 × 0.04 × 3 = $60
Lesson: Simple interest →
Compound interest
Learn it
A = P(1 + rn)^nt
Example: $1,000 at 5% a year, compounded yearly, for 2 years: A = 1,000 × 1.05² = $1,102.50
Percent change
Learn it
new − oldold × 100
Example: a $40 shirt marked down to $30: (30 − 40) ÷ 40 × 100 = −25%, a 25% decrease
Total cost
On GED sheet
total cost = (number of units) × (price per unit)
Example: 6 notebooks at $2.50: 6 × 2.50 = $15
Distance
On GED sheet
d = rt
Example: 60 mph for 2.5 hours: d = 60 × 2.5 = 150 miles

Data and probability

Mean (average)
On GED sheet
mean = sum of the valuesnumber of values
Example: tips of $40, $55, $35, $50, $45: 225 ÷ 5 = $45
Median
On GED sheet
median = the middle value, in order
Example: 3, 9, 4, 7, 5 in order: 3, 4, 5, 7, 9, so the median is 5
Probability
Learn it
P = ways it can happentotal number of outcomes
Example: 3 red socks in a drawer of 12: P = 3/12 = 1/4 = 0.25

Exponent rules

Multiplying: add the exponents
Learn it
a^m × aⁿ = a^{m + n}
Example: 2³ × 2⁴ = 2⁷ = 128
Dividing: subtract the exponents
Learn it
a^m ÷ aⁿ = a^{m − n}
Example: 5⁶ ÷ 5⁴ = 5² = 25
Power of a power: multiply them
Learn it
(a^m)ⁿ = a^mn
Example: (3²)³ = 3⁶ = 729

Here’s the part nobody warns you about: the GED gives you a formula sheet, but it leaves out 8 formulas you still need. This sheet has all 41, marks those 8 and works every one out with real numbers.

Coach Crissy

Math instructor

Published: October 20, 2026
Reading time: 4 min read

How to use the sheet: two quick examples

First decide what the question asks for: the space inside, the distance around, or a change. Then write down what each letter equals before you plug in.

Pick the formula, then the letters

On the GED sheet

A round rug is 6 feet across. How much floor does it cover? Use 3.14 for π.

The working

“How much floor” means area, so use the circle’s area: A = πr².
6 feet across is the diameter. The radius is half of it: r = 3.
Plug in: A ≈ 3.14 × 3² = 3.14 × 9 = 28.26.

Answer: about 28.26 square feet

A formula the GED leaves out

Learn it

Your rent goes from $800 to $840 a month. What is the percent increase?

The working

Use percent change: (new − old) ÷ old × 100.
Find the change: 840 − 800 = 40.
Divide by the old rent and multiply by 100: 40 ÷ 800 × 100 = 5.

Answer: 5%

The official GED sheet vs. this one

On test day you get the official GED formula sheet for the whole math test. 33 of the 41 formulas here are on it, marked “On GED sheet”.

The other 8, marked “Learn it”, aren’t: compound interest, percent change, the distance and midpoint between two points, probability and the exponent rules. Learn those before test day.

Want the official sheet itself, explained formula by formula? See the GED math formula sheet guide.

3 mistakes that cost points

Mistake 1: dropping the ½ or the ⅓

A triangle is half a rectangle, so its area has a ½. A cone holds a third of a cylinder the same size, so its volume has a ⅓. Leave either out and your answer is 2 or 3 times too big.

Mistake 2: doing the steps in the wrong order

In the trapezoid formula, add the two bases first. In compound interest, do the exponent before you multiply by P. The order of operations still rules inside a formula.

Mistake 3: using d = rt for two points on a graph

d = rt is for travel: speed times time. The distance between two points on a grid needs the distance formula, or a right triangle and the Pythagorean theorem.

Keep going

Written by

Coach Crissy

Math instructor

Coach Crissy teaches the video lessons behind the BooknBoost GED math course, working through GED-style problems on camera: ratios and proportions, percent and interest, mean, median and mode, slope, and the geometry students meet on test day.

Math Formula Sheet

41 formulas for GED math, each with a worked example. Geometry is on this page; lines, quadratics, money and data are on the next.

BooknBoost

On GED sheet 33 formulas the official GED formula sheet gives youLearn it 8 it leaves out: learn theseπ ≈ 3.14 in every example

Area

SquareA = s²On GED sheets = 6 in: A = 6² = 36 sq in

RectangleA = lwOn GED sheet12 ft by 9 ft: A = 12 × 9 = 108 sq ft

ParallelogramA = bhOn GED sheetb = 10 cm, h = 4 cm: A = 10 × 4 = 40 sq cm

TriangleA = 12bhOn GED sheetb = 8 m, h = 5 m: A = ½ × 8 × 5 = 20 sq m

TrapezoidA = 12h(b₁ + b₂)On GED sheetb₁ = 6 ft, b₂ = 10 ft, h = 4 ft: A = ½ × 4 × (6 + 10) = 2 × 16 = 32 sq ft

CircleA = πr²On GED sheetr = 3 in: A ≈ 3.14 × 3² = 3.14 × 9 = 28.26 sq in

Perimeter and circumference

SquareP = 4sOn GED sheets = 9 ft: P = 4 × 9 = 36 ft

RectangleP = 2l + 2wOn GED sheet15 yd by 8 yd: P = 2(15) + 2(8) = 30 + 16 = 46 yd

TriangleP = s₁ + s₂ + s₃On GED sheetsides 5, 7 and 9 cm: P = 5 + 7 + 9 = 21 cm

Circle (circumference)C = 2πr or C = πdOn GED sheetd = 20 in: C ≈ 3.14 × 20 = 62.8 in

Right triangles

Pythagorean theorema² + b² = c²On GED sheetlegs 5 and 12: c² = 25 + 144 = 169, so c = √169 = 13

Before you plug in

r is the radius, half the diameter. Given d = 10, use r = 5.

h is the straight-up height, never a slanted side.

B is the area of the base, p the perimeter of the base, and s the slant height.

Volume

Rectangular prism (box)V = lwhOn GED sheetl = 10, w = 4, h = 3 in: V = 10 × 4 × 3 = 120 cu in

Right prismV = BhOn GED sheetB = 15 sq cm, h = 6 cm: V = 15 × 6 = 90 cu cm

CylinderV = πr²hOn GED sheetr = 2 ft, h = 5 ft: V ≈ 3.14 × 2² × 5 = 62.8 cu ft

PyramidV = 13BhOn GED sheetB = 36 sq m, h = 5 m: V = (36 × 5) ÷ 3 = 60 cu m

ConeV = 13πr²hOn GED sheetr = 3 cm, h = 4 cm: V ≈ (3.14 × 3² × 4) ÷ 3 = 113.04 ÷ 3 = 37.68 cu cm

SphereV = 43πr³On GED sheetr = 3 in: V ≈ (4 × 3.14 × 3³) ÷ 3 = 339.12 ÷ 3 = 113.04 cu in

Surface area

Rectangular prism (box)SA = 2lw + 2lh + 2whOn GED sheeta 5 × 4 × 2 box: SA = 2(20) + 2(10) + 2(8) = 76 sq units

Right prismSA = ph + 2BOn GED sheetp = 12, h = 10, B = 6: SA = 12 × 10 + 2 × 6 = 132 sq units

CylinderSA = 2πrh + 2πr²On GED sheetr = 2, h = 5: SA ≈ 62.8 + 25.12 = 87.92 sq units

PyramidSA = 12ps + BOn GED sheet6 by 6 base, s = 5: SA = ½ × 24 × 5 + 36 = 96 sq units

ConeSA = πrs + πr²On GED sheetr = 3, s = 5: SA ≈ 47.1 + 28.26 = 75.36 sq units

SphereSA = 4πr²On GED sheetr = 2: SA ≈ 4 × 3.14 × 2² = 50.24 sq units

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Math Formula Sheet continued

Lines and graphs, quadratics, money and percents, data and probability, and the exponent rules.

BooknBoost

Lines and graphs

Slopem = y₂ − y₁x₂ − x₁On GED sheet(1, 2) and (4, 11): m = (11 − 2) ÷ (4 − 1) = 9 ÷ 3 = 3

Slope-intercept formy = mx + bOn GED sheet$45 a month plus $6 a gig: y = 6x + 45; 3 gigs: y = 6(3) + 45 = $63

Point-slope formy − y₁ = m(x − x₁)On GED sheetslope 2 through (3, 5): y − 5 = 2(x − 3), so y = 2x − 1

Distance between two pointsd = √((x₂ − x₁)² + (y₂ − y₁)²)Learn it(1, 2) and (4, 6): d = √(3² + 4²) = √25 = 5

MidpointM = (x₁ + x₂2, y₁ + y₂2)Learn it(2, 3) and (8, 7): M = (10 ÷ 2, 10 ÷ 2) = (5, 5)

Quadratics

Standard formy = ax² + bx + cOn GED sheety = 2x² − 3x + 1: a = 2, b = −3, c = 1

Quadratic formulax = −b ± √(b² − 4ac)2aOn GED sheetx² + 2x − 8 = 0: x = (−2 ± √36) ÷ 2 = (−2 ± 6) ÷ 2, so x = 2 or x = −4

Exponent rules

Multiplying: add the exponentsa^m × aⁿ = a^{m + n}Learn it2³ × 2⁴ = 2⁷ = 128

Dividing: subtract the exponentsa^m ÷ aⁿ = a^{m − n}Learn it5⁶ ÷ 5⁴ = 5² = 25

Power of a power: multiply them(a^m)ⁿ = a^mnLearn it(3²)³ = 3⁶ = 729

Money, percents and rates

Simple interestI = PrtOn GED sheet$500 at 4% for 3 years: I = 500 × 0.04 × 3 = $60

Compound interestA = P(1 + rn)^ntLearn it$1,000 at 5% a year, compounded yearly, for 2 years: A = 1,000 × 1.05² = $1,102.50

Percent changenew − oldold × 100Learn ita $40 shirt marked down to $30: (30 − 40) ÷ 40 × 100 = −25%, a 25% decrease

Total costtotal cost = (number of units) × (price per unit)On GED sheet6 notebooks at $2.50: 6 × 2.50 = $15

Distanced = rtOn GED sheet60 mph for 2.5 hours: d = 60 × 2.5 = 150 miles

Data and probability

Mean (average)mean = sum of the valuesnumber of valuesOn GED sheettips of $40, $55, $35, $50, $45: 225 ÷ 5 = $45

Medianmedian = the middle value, in orderOn GED sheet3, 9, 4, 7, 5 in order: 3, 4, 5, 7, 9, so the median is 5

ProbabilityP = ways it can happentotal number of outcomesLearn it3 red socks in a drawer of 12: P = 3/12 = 1/4 = 0.25

Check the units

Perimeter and circumference are plain units (ft). Area is square units (sq ft). Volume is cubic units (cu ft).

On test day

You get the official formula sheet for the whole GED math test, even the questions without a calculator. The formulas marked Learn it aren’t on it.

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