Decimals, Fractions & Percents
Convert between decimals, fractions, percents and mixed numbers.
Adding and Subtracting Fractions Calculator
Add or subtract 2 to 10 fractions at once with the least common denominator (LCD) method, showing every conversion, reduction, and mixed-number step.
Adding and Subtracting Integers Calculator
Add and subtract positive and negative integers step by step, with the Keep-Change-Change rule for subtracting a negative and clear sign rules.
Averaging Fractions Calculator
Average 2 to 10 fractions, mixed numbers, whole numbers, or decimals at once with exact LCD arithmetic, showing every sum, reduction, and divide-by-n step.
Circular Permutations Calculator
Find the number of ways to arrange n distinct items around a circle — (n−1)! — with the fix-a-reference-point reasoning and a comparison to a straight line.
Combinations Calculator (nCr)
Calculate C(n,r), the number of unordered ways to choose r items from n, using nCr = n!/(r!(n−r)!), the nPr/r! relation, and the symmetry rule.
Combinations with Replacement Calculator (CR)
Calculate CR(n,r) = C(n+r−1,r), the number of unordered selections of r items from n types with repeats allowed, via stars and bars, steps shown.
Common Factors Calculator
Find every common factor shared by a list of whole numbers, plus the GCF, with a step-by-step divisor list for each value and their overlap.
Comparing Fractions Calculator
Compare two fractions, mixed numbers, or decimals to see which is less than, greater than, or equal — with LCD, decimal, and cross-multiplication methods shown.
Complex Fraction Calculator
Simplify a complex fraction (a/b)/(c/d) into a single fraction, step by step, using "keep, change, flip" and automatic mixed-number conversion.
Decimal to Fraction Calculator
Convert any decimal to a fraction or mixed number in lowest terms — including repeating decimals like 0.333… — with full step-by-step working.
Decimal to Percent Converter
Convert any decimal to a percentage instantly. Free, accurate, step-by-step decimal-to-percent calculator with worked examples and reverse conversion.
Diamond Problem Solver
Solve the diamond problem — enter two factors to get their product and sum, or enter a product and sum to find the two factors that multiply and add to them.
Equivalent Fractions Calculator
Find fractions equal in value to any fraction by multiplying the numerator and denominator by the same number, with 20 equivalents and every step shown.
Discount Calculator
Free discount calculator: enter any two of list price, sale price, and discount percent to find the third, plus the amount you save.
Estimating Fractions Calculator (Sums & Differences)
Estimate the sum or difference of two fractions or mixed numbers by rounding each to the nearest 0, 1/2, or 1 — then compare it with the exact answer.
Even/Odd Permutations Calculator
Split the n! permutations of n distinct items into even and odd classes — always exactly n!/2 each — with the transposition-parity reasoning and steps.
Expanded Form Calculator (with Word Form)
Write a number in expanded form three ways — notation, factors, and exponential — plus word form. Shows each digit times its place value, step by step.
Factorial Calculator (n!)
Calculate n factorial (n!) instantly with the full multiplication chain shown. Handles huge results in scientific notation and explains why 0! equals 1.
Factoring Calculator
Find every factor of a number — all divisors and factor pairs — with step-by-step trial division up to the square root. Negatives and primes handled.
Fraction to Decimal Calculator
Convert any fraction or mixed number to a decimal with step-by-step long division. Detects repeating decimals and shows them in bar notation.
Fibonacci Sequence Calculator
Generate the Fibonacci sequence, find F(n) instantly, and watch the ratio of consecutive terms converge toward the golden ratio φ ≈ 1.618.
Fraction to Percent Calculator
Convert any fraction or mixed number to a percentage with step-by-step working. Handles repeating decimals exactly with bar notation.
Fractions Calculator
Add, subtract, multiply, or divide two fractions with step-by-step cross-multiplication, automatic reduction, and mixed-number conversion.
Fractions Number Line: Visualize Fractions on 0-1
See fractions plotted on a number line from 0 to 1, one row per denominator, with equivalent fractions aligning vertically, plus a fraction highlighter.
Fractions Table: Decimal & Percent Reference Chart
Browse a fractions table from 1/2 up to 1/16, sorted by value, with each row's decimal, percent, and equivalent fractions — plus a fraction highlighter.
GCF Calculator (Greatest Common Factor)
Find the greatest common factor (GCF) of two or more numbers, explained three ways: prime factorization, listing divisors, and Euclid's algorithm.
Golden Ratio Calculator — Solve for A, B, or A + B
Calculate the golden ratio φ ≈ 1.618 from one value — the longer segment (A), shorter segment (B), or their sum (A+B) — with the other two and full steps.
Improper Fraction to Mixed Number Calculator
Convert any improper fraction to a mixed number in lowest terms with full step-by-step working. Supports negative fractions — exact BigInt math, no rounding.
Lattice Multiplication Calculator
Multiply numbers with the lattice (Gelosia) method — a grid of diagonally split cells summed along diagonals, shown step by step with the full lattice.
LCD Calculator (Least Common Denominator)
Find the least common denominator (LCD) of fractions, mixed numbers, and integers, then rewrite each one as an equivalent fraction over that LCD.
LCM Calculator (Least Common Multiple)
Find the least common multiple (LCM) of two or more numbers, explained three ways: prime factorization, the GCF formula, and listing multiples.
Long Addition Calculator
Add two or more whole numbers or decimals in columns with carrying, shown step by step — every place-value column, each carry, and the final sum.
Long Division Calculator (with Remainders)
Divide whole numbers with the long-division bracket, shown step by step — Divide, Multiply, Subtract, Bring down — with the quotient, remainder, and a check.
Long Division with Decimals Calculator
Divide numbers into decimal places with long division — move the decimal point, bring down zeros, and calculate to any place count (truncated, not rounded).
Long Multiplication Calculator
Multiply numbers with the standard algorithm, shown step by step — partial products, place-value shifts, decimal-point placement, and the sign rule.
Long Subtraction Calculator (with Borrowing)
Subtract numbers in columns with borrowing and regrouping, shown step by step — including chained borrows across zeros and a built-in addition check.
Mixed Number to Decimal Calculator
Convert any mixed number to a decimal with two solution methods and adjustable rounding. Step-by-step long division and improper-fraction breakdown.
Mixed Number to Percent Calculator
Convert any mixed number to a percent with two solution methods. Shows the decimal step, multiplies by 100, and rounds to your chosen precision.
Mixed Numbers Calculator
Add, subtract, multiply, or divide two mixed numbers, whole numbers, or fractions — see every improper-fraction step and the reduced, mixed-number answer.
Mixed Number to Improper Fraction Calculator
Convert any mixed number to an improper fraction with the formula (a×c+b)/c. Step-by-step solution, simplified form, and dozens of worked examples.
Money Math Calculator
Add, subtract, multiply, split, and stretch money to the cent. Column layouts for dollars-and-cents, even splits rounded down, and how many items a budget buys.
Multifactorial Calculator (n!!, n!!!)
Calculate the multifactorial n!!, n!!! or any step-k factorial, with the full multiplication chain shown. Clears up the classic n!! vs (n!)! mix-up.
Modulo Calculator
Compute a mod b — the remainder left over after dividing a by b — with the quotient, the check identity, and a step-by-step divisibility test shown.
Multiples Calculator
List the multiples of any positive integer, up to 1,000 at a time, optionally starting above a chosen minimum, with the formula shown step by step.
Order of Operations Calculator (PEMDAS)
Solve any expression in the correct order — PEMDAS / BODMAS — one step at a time. Supports exponents, roots, and three kinds of brackets.
Ordering Fractions Calculator
Arrange 2 to 15 fractions, mixed numbers, whole numbers, and decimals from least to greatest or greatest to least, with the LCD method shown step by step.
Pascal's Triangle Generator
Build Pascal's triangle row by row — every number is the sum of the two above it. See row sums, binomial coefficients, and the hidden diagonals explained.
Percent Error Calculator
Free percent error calculator. Compare an experimental (measured) value against a theoretical (actual) value, with step-by-step working.
Percent to Decimal Converter
Convert any percent to a decimal instantly. Free, step-by-step percent-to-decimal calculator with worked examples and reverse decimal-to-percent conversion.
Percent to Fraction Calculator
Convert any percent to a simplified fraction with a five-step working — including decimal percents like 12.5% and improper percents like 150%.
Percentage Calculator
Free percentage calculator for all three percent problems: find P% of a number, find what percent Y is of X, or find the whole number from a part and percent.
Percentage Change Calculator
Free percentage change calculator. Find the percent increase or decrease between an initial value and a new value, with step-by-step working.
Percentage Difference Calculator
Free percentage difference calculator. Compare two values with no before-or-after order and find the % difference relative to their average.
Percentage Decrease Calculator
Free percentage decrease calculator. Find how much a value shrank from a starting value to a final value, as a percent, with step-by-step working.
Percentage Increase Calculator
Free percentage increase calculator. Find how much a value grew from a starting value to a final value, as a percent, with step-by-step working.
Permutations Calculator (nPr)
Calculate P(n,r), the number of ordered arrangements of r items chosen from n, with the n!/(n−r)! formula, factorial cancellation, and step-by-step work shown.
Permutations with Replacement Calculator (n^r)
Calculate PR(n,r) = n^r, the number of ordered arrangements of r positions where each pick can repeat — PIN codes, passwords, license plates — with steps shown.
Place Value Calculator
Find the place value of every digit in a number — ones, tens, tenths, and beyond — with a digit-by-digit table, word form, and an addition check.
Prime Factorization Calculator
Break any integer into its prime factors by trial division, shown as a full division chain and in exponent form like 2² × 5².
Prime Number Calculator
Check whether any whole number is prime or composite using step-by-step square-root trial division, and see the nearest primes on either side of it.
Ratio Calculator: Solve A : B = C : D
Solve the missing term in a ratio proportion A:B = C:D by cross-multiplication. Enter three positive numbers and get the fourth, exact and step by step.
Ratio Simplifier Calculator
Simplify a ratio like A:B or A:B:C:D to its lowest integer terms — handles whole numbers, decimals, fractions, and mixed numbers, with full steps.
Ratio to Fraction Calculator
Convert a ratio A:B into a simplified fraction — pick part-to-part (find the whole by adding) or part-to-whole (B is already the whole) — with full steps.
Roman Numeral Calculator (Convert and Calculate)
Convert between Roman numerals and numbers, or add, subtract, multiply, and divide them. Shows the symbol breakdown and the classic Roman addition steps.
Round to the Nearest Multiple Calculator
Round any number to the nearest multiple — 5, 25, 0.05, a dozen — using round(x ÷ m) × m, shown step by step with the neighboring multiples.
Rounding Methods Calculator (9 Methods)
Compare all 9 rounding methods side by side — Half Up, Down, Even, Odd, Away, Toward, Ceiling, Floor, Random — and see how each handles an exact halfway value.
Rounding Numbers Calculator
Round a number to any place from millions to millionths, step by step. See the target digit, the deciding digit, and the direction, using Half Away From Zero.
Sales Tax Calculator
Free sales tax calculator: enter pre-tax price and tax rate to find the tax and total, or work backward to find the pre-tax price or rate.
Scientific Notation Operations Calculator
Add, subtract, multiply, and divide numbers in scientific notation step by step. Lines up exponents, normalizes the result, and shows every format.
Scientific Notation Converter
Convert any number to and from scientific notation, e-notation, engineering notation, order of magnitude, and word form — with the decimal-point steps.
Significant Figures Calculator
Add, subtract, multiply, or divide with significant figures. See each input's sig figs, the exact result, and the correctly rounded reported value.
Simplifying Complex Fractions Calculator
Simplify X/Y where X and Y can each be a whole number, fraction, mixed number, or decimal, with full "convert, multiply by the reciprocal" steps shown.
Simplify Fractions Calculator
Reduce any fraction to its lowest terms using the greatest common factor, convert improper results to a mixed number, and see every step worked out.
Solve for X in a Proportion Calculator
Solve the unknown x in a proportion like x/4 = 3/8 using cross-multiplication, with the exact fraction, mixed number, and decimal shown step by step.
Speed Distance Time Calculator
Solve for speed, distance, or time from the other two, step by step. Enter time as hours or hh:mm:ss, and see the formula triangle that links them.
Standard Form Calculator
Convert numbers to and from standard form (A × 10ⁿ) step by step. Standard form is the British term for scientific notation, keeping significant zeros.
Unit Rate Calculator
Find the unit rate — the amount per one unit — by dividing two quantities. See the ratio scaled to per 1 and the division, step by step, with worked examples.
Tip Calculator
Free tip calculator: enter the bill and a tip percent to get the tip amount, the total, and an even split per person for any size group.
Vote Percentage Calculator
Free vote percentage calculator: enter votes for up to 12 candidates, parties, or options and instantly see each one's exact share of the total vote.