A formula sheet is a page of math formulas that a test or class gives you, so you do not have to memorize them: area and volume formulas, slope and the quadratic formula. The GED math test provides one with lines such as A = π r2 and d = rt. You still have to choose the right formula and use it correctly.
In Spanish
hoja de fórmulas
Also called
reference sheet, formula chart, formula page, mathematics reference sheet
The sheet hands you the formulas. The points come from what you add: picking the right one, plugging in the right numbers and rearranging when needed.
Formal definition and notation
A formula sheet (also called a reference sheet) is an official list of formulas supplied with an assessment or course. It states each formula and the meaning of its letters, but not which problems need it, how to rearrange it, or how to handle units. Which formulas appear, and whether a sheet is given at all, depends on the test, so students should check their own test’s materials before test day.
Symbol
Read it as
Meaning
π ≈ 3.14
pi is about 3.14
the value of π a sheet may tell you to use
B
capital B
on volume formulas, the area of the base, not the base length
A sheet lists each formula once, in one form. Rearranging it (for example, t = dr) is your job.
Read the letters carefully: r is a radius, not a diameter; capital B is a base area.
Rates in a formula are decimals: r = 0.04 for 4% interest.
Knowing the sheet before test day saves time: find where each formula is, and memorize anything your test does not provide.
Formula Sheet examples, step by step
Example 1: Use a volume formula
Warm-up
The formula sheet gives V = π r2h for a cylinder. Find the volume of a can with radius 3 cm and height 10 cm.
Substitute: V = π (3)2(10).
32 = 9, and 9 × 10 = 90, so V = 90π.
Use π ≈ 3.14: 90 × 3.14 = 282.6.
Answer: The volume is 90π, about 282.6 cubic centimeters.
Example 2: Rearrange a formula from the sheet
Core
The sheet gives I = Prt. A loan of 1,500 dollars at 4% simple interest earns 180 dollars of interest. How many years is the loan?
Solve for t: t = IPr.
Write 4% as a decimal: r = 0.04.
t = 1801500 × 0.04 = 18060 = 3.
Answer: The loan lasts 3 years.
Example 3: Radius, not diameter
Test-style
The sheet gives V = 43π r3 for a sphere. A ball has a diameter of 6 inches. What is its volume, to the nearest cubic inch?
The formula needs the radius: r = 6 ÷ 2 = 3 in.
V = 43π (3)3 = 43π × 27 = 36π.
36π ≈ 113.1, which rounds to 113.
Using 6 for r would give 288π ≈ 905, the classic trap.
Answer: The volume is 36π, about 113 cubic inches.
Common mistakes
✗ MistakeFor a circle with diameter 10, A = π (10)2 = 100π.
✓ Insteadr = 5, so A = π (5)2 = 25π.
Sheet formulas use the radius. A diameter in the problem must be halved first, or the area comes out 4 times too big.
✗ MistakeI = Prt with 2,000 dollars at 5% for 2 years: 2000 × 5 × 2 = 20,000 dollars.
✓ InsteadI = 2000 × 0.05 × 2 = 200 dollars.
The rate is a percent, so write it as a decimal before multiplying. 20,000 dollars of interest on a 2,000 dollar loan should look wrong.
✗ MistakeThe sheet has every formula I could need, so I do not need to study formulas.
✓ InsteadThe sheet lists formulas, not methods. You still need to know what each letter means, when to use each formula, and facts the sheet may not include.
Test writers expect you to choose, rearrange and combine formulas. Practicing with the sheet is part of studying.
A formula is one equation that relates quantities, like A = lw. A formula sheet is a collected page of many formulas.
Formula Sheetvs.Notes or cheat sheet
A formula sheet is supplied officially by the test. Personal notes are usually not allowed in the testing room unless the rules say so.
Quick check: 3 questions
Question 1 of 3
The formula sheet gives A = 12bh. A triangle has base 14 cm and height 9 cm. What is its area?
Show answer and explanation
Answer: C.12 × 14 × 9 = 63 cm². 126 forgets the one half, 23 adds, and 31.5 takes half twice.
Question 2 of 3
The sheet gives d = rt. A cyclist rides 54 miles at 12 mph. Which step finds the time?
Show answer and explanation
Answer: B. Divide both sides of d = rt by r: t = dr = 54 ÷ 12 = 4.5 hours. A multiplies, C divides the wrong way, and D subtracts.
Question 3 of 3
The sheet gives V = π r2h. A cylinder has diameter 8 m and height 5 m. What is its volume?
Show answer and explanation
Answer: D.r = 4, so V = π × 16 × 5 = 80π. 320π uses the diameter as the radius, 40π forgets to square, and 160π doubles the answer.
Formula Sheet: frequently asked questions
Does the GED give you a formula sheet?
Yes. The GED mathematical reasoning test comes with a formula sheet that lists area, perimeter, surface area and volume formulas, data formulas such as mean and median, and algebra formulas including slope, the quadratic formula, the Pythagorean theorem, simple interest and distance. Practicing with that exact sheet before the test helps you find formulas quickly.
What formulas should I memorize if a sheet is provided?
Anything your test does not list. Many students also memorize the most used formulas, such as area of a rectangle and triangle, the slope formula and d = rt, to save time. Learn what every letter means, how to rearrange each formula, and basic facts such as unit conversions and percent-to-decimal changes.
Why do students still miss formula sheet questions?
Most errors happen after the formula is found: using a diameter instead of a radius, forgetting to change a percent to a decimal, mixing units, or not rearranging the formula for the unknown. Write the formula, list each value with its unit, substitute, and check that the answer is reasonable.
Updated November 2026·Reviewed by the Effortless Math team·Standards: n/a
Cite this entry
Effortless Math Team. “Formula Sheet.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/formula-sheet/
Flashcard
TermFormula SheetA = π r2, d = rt, I = Prt
DefinitionAn official page of formulas given with a test. It lists formulas; you choose one, plug in correct values (radius, decimal rate) and rearrange.
FormulaA formula is a rule written with symbols that shows how quantities are related. It is an equation with two or more variables, such as A = lw for the area of a rectangle. Formulas help solve problems the same way each time: substitute the values you know, then compute the one you need.Problem Solving · Grade 5, Grade 6, Grade 7VolumeVolume measures the amount of space inside a three-dimensional figure, in cubic units such as cubic centimeters or cubic feet. You can find it by counting the unit cubes that fill the solid. For a rectangular prism, V = l × w × h; for any prism, it equals the area of the base multiplied by the height.Geometry · Grade 5, Grade 6, Grade 7LengthLength is how long something is: the distance from one end of an object to the other. You measure it by counting equal units laid end to end with no gaps or overlaps, such as inches, feet, centimeters or meters. A new pencil is about 7 inches long.Measurement · Grade 1, Grade 2, Grade 3Surface AreaSurface area is the total area of all outside faces of a three-dimensional figure, measured in square units. To find it, unfold the solid into a flat net, find the area of each face and add them. A box with length l, width w and height h has surface area 2lw + 2lh + 2wh.Geometry · Grade 6, Grade 7, Grade 8PerimeterPerimeter is the total distance around a two-dimensional shape. To find it, add the lengths of all the sides. A rectangle with sides 5 and 3 has perimeter 5 + 3 + 5 + 3 = 16. Perimeter is a length, so it uses length units such as inches or meters, never square units.Geometry · Grade 3, Grade 4, Grade 5MedianThe median is the middle value when data are listed in order. If there is an even number of values, the median is the average of the two middle values. Half the data lie at or below the median and half at or above it, and outliers barely move it.Statistics · Grade 5, Grade 6, Grade 7SlopeSlope is a number that measures how steep a line is: the change in y divided by the change in x between any two points on the line, often called rise over run. A positive slope rises from left to right, a negative slope falls, and a horizontal line has slope 0.Algebra · Grade 8, Algebra 1Slope-Intercept FormSlope-intercept form is the linear equation form y = mx + b, where m is the slope and b is the y-intercept. You can read both values directly from the equation without rearranging: in y = 2x + 5, the slope is 2 and the line crosses the y-axis at (0, 5).Algebra · Grade 8, Algebra 1Quadratic FormulaThe quadratic formula gives the solutions of any quadratic equation ax2 + bx + c = 0 with a ≠ 0: x = −b ± √b2 − 4ac2a. Substitute a, b and c, then compute once with plus and once with minus. It works even when the quadratic cannot be factored.Algebra · Algebra 1, Algebra 2Pythagorean TheoremThe Pythagorean theorem says that in a right triangle, a2 + b2 = c2. The legs are a and b, the two sides that form the right angle. The hypotenuse, c, is the longest side across from the right angle. Legs of 3 and 4 give 9 + 16 = 25, so the hypotenuse is 5.Geometry · Grade 8, Algebra 1RadiusThe radius is a line segment from the center of a circle to any point on the circle, or the length of that segment. The radius is half the diameter: if the diameter is 10, the radius is 5. All radii in the same circle have equal length, and r is the radius in C = 2π r.Geometry · Grade 6, Grade 7, Grade 8DiameterThe diameter of a circle is the distance straight across it through the center. It is twice the radius, d = 2r, and it is the longest chord any circle has. The word also names the line segment itself: a segment that passes through the center and touches both sides of the circle.Geometry · Grade 6, Grade 7, Grade 8CylinderA cylinder is a three-dimensional solid with two parallel, equal circular bases joined by one curved surface, like a soup can. Its size is set by the radius r of a base and the height h between the bases. Its volume is π r2h, the base area times the height.Geometry · Grade 1, Grade 8, GeometryVariableA variable is a letter or symbol that represents a number or value, usually one that can change or is not yet known. In n + 5 = 12, the variable n is an unknown that equals 7. In A = lw, the variables l and w can take many values. Any letter can be a variable, not just x.Algebra · Grade 6, Grade 7, Grade 8In Terms OfIn terms of means the answer should be written using a given variable or symbol. “Write the perimeter in terms of w” wants an expression with w, such as 4w + 10. “Solve for y in terms of x” means get y alone, with only x on the other side. “In terms of π” keeps π as a symbol: 9π, not 28.26.Problem Solving · Grade 7, Grade 8, Algebra 1ReasonablenessReasonableness is checking whether an answer makes sense for the problem before you accept it. Estimate first to see about how big the answer should be, then check the units and the context: a negative length, 3.5 people or 800 dollars for one pencil is not reasonable. A correctly calculated number can still fail this check.Problem Solving · Grade 3, Grade 4, Grade 5AreaArea is the amount of surface a flat shape covers, measured in square units. It counts how many unit squares fit inside the shape, which is why the units are squared. A rectangle’s area is length times width, so a 5 by 3 rectangle has area 15 square units.Geometry · Grade 3, Grade 4, Grade 5Distance-Rate-Time FormulaThe distance-rate-time formula is d = rt: distance equals rate (speed) times time, for anything moving at a constant rate. Solve it for the other two letters to get r = dt and t = dr. Driving at 45 miles per hour for 3 hours covers 45 × 3 = 135 miles.Problem Solving · Grade 6, Grade 7, Algebra 1PrincipalThe principal is the original amount of money that is borrowed, deposited or invested, before any interest is added. In the simple interest formula I = Prt, the letter P stands for the principal. Deposit 2,000 dollars at 3% simple interest for 4 years: the principal is 2,000 dollars, the interest is 240 dollars, and the total is 2,240 dollars.Problem Solving · Grade 7, Algebra 1