Lessons, not the tool list
Free Math Guides
Last updated: October 2026
Written by Jessica Hill
These are the written lessons: the formula, a worked example, and the mistakes that change the answer. If you already know the method and only need the calculator, open the tools directory.
Start here
The Lessons People Open First
Each one includes the calculator for that method.
- PercentageWhy “percent of,” “percent change,” and “what percent” are three different calculations.Read the lesson
- Fraction CalculatorHow to add, subtract, multiply, and divide fractions without skipping the common denominator.Read the lesson
- GPAHow credits turn letter grades into one 4.0 average, including honors and AP.Read the lesson
- Pythagorean TheoremHow a² + b² = c² finds the missing side, and how to check that the triangle is right.Read the lesson
Everyday Math
Percentages, fractions, time, and the calculations people use outside of class.
- PercentageWhy “percent of,” “percent change,” and “what percent” are three different calculations.
- Fraction CalculatorHow to add, subtract, multiply, and divide fractions without skipping the common denominator.
- Fraction SimplifierHow the greatest common factor reduces a fraction, and when the result is a mixed number.
- Decimal to FractionHow a terminating or repeating decimal becomes a fraction in lowest terms.
- RoundingWhich digit decides the round, and how significant figures differ from decimal places.
- Unit ConverterHow to convert a measurement by multiplying by one, written as a fraction of units.
- TipHow a tip percentage becomes a dollar amount, and how to split the total.
- DiscountHow a markdown changes the price, including a second discount on the sale price.
- Times TablesHow a times table is built, and how to use it to check multiplication.
- Long DivisionHow long division produces a quotient, a remainder, and a decimal.
- AgeHow to count years and days between two dates, including a birthday that has not happened yet.
- Roman NumeralsHow the subtractive pairs, such as IV and IX, change a number into a Roman numeral.
- Roman numeralsGuideThe seven symbols, the four rules, and how to read a year such as MMXXVI.
- Decimal to fractionGuideHow to turn a decimal into a fraction, including a repeating decimal.
- Equivalent fractionsGuideWhy 1/2, 2/4, and 4/8 are the same amount, and how to check.
- PEMDASGuideThe order of operations, and why multiplication does not always come before division.
Algebra
Equations, factors, exponents, and the formulas that solve them.
- Equation SolverHow to isolate a variable in a linear equation, a quadratic, or a two-equation system.
- Quadratic SolverHow the discriminant tells you how many real roots the formula will return.
- AlgebraHow to evaluate an expression, solve ax + b = c, and factor a simple polynomial.
- FactorsHow to list factor pairs and break a number into primes.
- LCMHow to find the smallest shared multiple, and why that number is the LCD of two fractions.
- GCFHow to find the largest shared factor, and how that factor simplifies a fraction.
- ExponentHow to expand a power, use eˣ, and solve for a missing exponent.
- LogarithmHow a logarithm answers “10 to what power,” and when the base is e instead.
- Square RootHow to simplify a square root, and what an nth root means.
- MatrixHow to add, multiply, and invert a 2×2 matrix by hand.
- Quadratic formulaGuideHow to solve ax² + bx + c = 0 in five steps, including the discriminant.
- Prime numbersGuideWhat makes a number prime, the list to 100, and how to test one by hand.
- Fibonacci sequenceGuideHow each number is the sum of the two before it, and where the golden ratio appears.
Geometry
Shapes, distance, slope, and how a picture becomes a number.
- Pythagorean TheoremHow a² + b² = c² finds the missing side, and how to check that the triangle is right.
- TriangleHow to finish a triangle when you know two sides, the area, or two angles.
- AreaHow the area formula changes for a rectangle, a triangle, a circle, and a room.
- SlopeHow two points give a rise-over-run slope, and what a percent grade means.
- GraphingHow a function becomes a table of points, and where it crosses the axes.
- Pythagorean theoremGuideThe formula, four proofs, triples, and how to test for a right angle.
Trigonometry
Angles, the unit circle, and how sine and cosine get their values.
Statistics
Averages, spread, and how likely an outcome is.
- StatisticsHow mean, median, mode, and standard deviation describe one list in different ways.
- Mean, Median, ModeWhen the mean, the median, and the mode disagree, and which one to report.
- Standard DeviationThe difference between dividing by n and dividing by n − 1.
- Z-ScoreHow many standard deviations a value sits from the mean, and what a percentile says.
- ProbabilityHow “and,” “or,” and the complement change the chance of an event.
- ProbabilityGuideThe basic formula, the main rules, and worked examples with dice and cards.
- Mean, median, and modeGuideHow to find each one, and which one to use when a list has an outlier.
Calculus
Rates of change, accumulated area, and what a limit is saying.
School And Money
Grades, GPA, scientific notation, and how interest grows.
- GPAHow credits turn letter grades into one 4.0 average, including honors and AP.
- GradeHow category weights, a final exam, and a count of wrong answers each produce a class score.
- Scientific NotationHow to move the decimal point so a number is written as a × 10ⁿ.
- Compound InterestHow interest added to the balance changes the next period’s interest.
- Simple InterestHow simple interest stays on the original amount, unlike compound interest.
- BMIHow height and weight become a BMI, and what the WHO bands do and do not mean.
- How to calculate GPAGuideFour steps from letter grades and credits to a semester and cumulative GPA.
- Compound interestGuideHow interest on interest works, and what the compounding frequency changes.
- Scientific notationGuideHow to write a number as a value from 1 to 10 times a power of 10.
How This Site Works
These pages explain CalcSolver itself. They are not calculators, so they are not listed in Tools.
- Scientific calculatorWhat the scientific keys do, and when DEG and RAD give different answers.
- Calculus solverHow derivatives, integrals, and limits fit together before you open one calculator.
- Math solverWhat an equation, an expression, and a step-by-step solve each ask you to do.
- Calculator unblockedWhat “unblocked” means on a school network, and what still runs in the browser.
- CalcSolver namesHow this site differs from other sites that use the CalcSolver name.
- CalcSolver codesWhat the on-screen codes refer to, and which ones this site does not use.
- Code modeWhat code mode is on a handheld, and why this site does not need it.
- Calculator gameWhy a calculator game is separate from getting a math answer.
Already know the method? The tools directory opens the calculator without the lesson.
Tools And Guides Do Different Jobs
Tools is the calculator directory. You open a card and type your numbers. Guides is this library. You read how the method works, then use the calculator at the top of that lesson.
Frequently Asked Questions
What is the difference between Tools and Guides?
Tools lists the calculators. Guides explains the method: the formula, one worked example, and the mistakes that change the answer. The calculator for that method sits at the top of the lesson.
Do I need to open both?
No. Open Tools when you want an answer. Open Guides when you want to learn the steps or check homework.