Math Calculators
Free online math calculators for percentages, fractions, exponents, statistics, probability, and more. These tools cover arithmetic, algebra, number theory, and statistics with step-by-step solutions. Whether you need to find the LCM of two numbers, calculate standard deviation, or solve a proportion, these calculators provide instant, accurate results.
Percentage Calculator
Calculate percentages with 6 calculation types: find percentage of a number, percentage change, difference, increase, decrease, and reverse percentage.
Average Calculator
Calculate the mean, median, mode, range, geometric mean, and harmonic mean from a set of numbers with step-by-step breakdown.
Fractions Calculator
Add, subtract, multiply, or divide fractions with automatic simplification. Shows result as both fraction and decimal.
Exponents Calculator
Calculate the power of any number. Supports decimal bases, negative exponents, and shows results in scientific notation.
Log Calculator
Calculate logarithms with any base. Supports natural log (ln), log base 2, log base 10, and custom bases.
Square Root Calculator
Calculate square root, cube root, or any nth root. Shows whether the number is a perfect square or cube.
Factorial Calculator
Calculate the factorial of any integer from 0 to 170. Shows result, number of digits, and trailing zeros.
Scientific Notation Calculator
Convert between decimal and scientific notation. Shows decimal, scientific, and E-notation forms with arithmetic operations.
LCM Calculator
Calculate the Least Common Multiple of two or more numbers using prime factorization with step-by-step solution.
GCF Calculator
Calculate the Greatest Common Factor (GCD) of two or more numbers with prime factorization and division method.
Ratio Calculator
Solve ratio proportions (A:B = C:?) and simplify ratios to lowest terms. Supports scaling and equivalent ratios.
Proportion Calculator
Solve proportions by finding the missing value in A/B = C/D using cross multiplication with step-by-step solution.
Rounding Numbers Calculator
Round numbers to specified decimal places. Shows rounded, floor, ceiling, truncated, and nearest 10/100/1000 values.
Significant Figures Calculator
Count significant figures in any number. Shows which digits are significant with highlighted analysis and rounding.
Remainder Calculator
Calculate the remainder (modulo) when dividing two numbers. Shows quotient, remainder, and verification step.
Matrix Calculator
Perform matrix operations: add, subtract, multiply, determinant, transpose, and inverse for 2x2 and 3x3 matrices.
Prime Factorization Calculator
Find the prime factorization of any positive integer. Shows factor tree, all divisors, and primality check.
Combinations Calculator
Calculate combinations C(n,r) for choosing r items from n without regard to order. Shows formula breakdown.
Permutations Calculator
Calculate permutations P(n,r) for arranging r items from n where order matters. Compares with combinations.
Long Division Calculator
Perform long division with step-by-step solution. Shows quotient, remainder, decimal result, and verification.
Probability Calculator
Calculate probability for single events, complements, unions, intersections, and conditional probability with visual results.
Standard Deviation Calculator
Calculate standard deviation, variance, and coefficient of variation for population and sample data sets.
How to Use Math Calculators
Each math calculator is designed for a specific type of problem. For basic arithmetic, use the Percentage Calculator or Fractions Calculator. For number theory problems, try the LCM, GCF, or Prime Factorization calculators. For statistics, the Standard Deviation and Probability calculators provide detailed analysis. Simply enter your numbers, click Calculate, and get instant results with step-by-step explanations showing exactly how the answer was derived.
Common Math Formulas
Percentage: (Part / Whole) x 100
LCM(a,b) = |a x b| / GCF(a,b)
Combinations: C(n,r) = n! / (r!(n-r)!)
Permutations: P(n,r) = n! / (n-r)!
Standard Deviation: s = sqrt(Sum((xi - mean)^2) / (n-1))
Quadratic Formula: x = (-b +/- sqrt(b^2 - 4ac)) / 2a
These fundamental formulas underpin most calculations in algebra, statistics, and number theory. The combination and permutation formulas count arrangements with and without regard to order. Standard deviation measures data spread around the mean. Each calculator on this page applies the relevant formula automatically and shows the work.
Example Calculation
Find LCM of 12 and 18:
Step 1: Prime factorization
12 = 2^2 x 3
18 = 2 x 3^2
Step 2: Take highest power of each prime
2^2 = 4
3^2 = 9
Step 3: Multiply
LCM = 4 x 9 = 36
Verification: 36/12 = 3, 36/18 = 2 (both whole numbers)
Math Operations Reference Table
| Operation | Formula | Example | Result |
|---|---|---|---|
| Percentage | (Part/Whole) x 100 | 25/200 x 100 | 12.5% |
| Square Root | sqrt(x) | sqrt(144) | 12 |
| Factorial | n! | 5! | 120 |
| LCM | |a x b| / GCF | LCM(8,12) | 24 |
| GCF | Euclidean algorithm | GCF(48,36) | 12 |
| Combinations | n!/(r!(n-r)!) | C(10,3) | 120 |
| Permutations | n!/(n-r)! | P(10,3) | 720 |
| Log base 10 | log10(x) | log10(1000) | 3 |
| Natural Log | ln(x) | ln(e^2) | 2 |
| Exponent | x^n | 2^10 | 1024 |
Frequently Asked Questions
What is the difference between LCM and GCF?
LCM (Least Common Multiple) is the smallest number that both numbers divide into evenly. GCF (Greatest Common Factor) is the largest number that divides into both numbers evenly. For example, LCM(4,6) = 12 and GCF(4,6) = 2. They are related by the formula: LCM(a,b) x GCF(a,b) = a x b.
What is the difference between combinations and permutations?
Combinations count selections where order does not matter (choosing a committee), while permutations count arrangements where order matters (assigning positions). C(5,3) = 10 ways to choose 3 from 5, but P(5,3) = 60 ways to arrange 3 from 5. Permutations are always larger because each combination can be arranged in multiple ways.
How do significant figures work?
Significant figures indicate the precision of a measurement. All non-zero digits are significant. Zeros between non-zero digits are significant. Leading zeros are not significant. Trailing zeros after a decimal point are significant. For example, 0.00450 has 3 significant figures (4, 5, and the trailing 0).
What is standard deviation used for?
Standard deviation measures how spread out data values are from the mean. A low standard deviation means values cluster near the average, while a high standard deviation means values are widely dispersed. It is used in statistics, quality control, finance (volatility), and science to quantify variability in data sets.
When should I use population vs sample standard deviation?
Use population standard deviation (divide by N) when your data includes every member of the group you are studying. Use sample standard deviation (divide by N-1) when your data is a subset of a larger population. The N-1 correction (Bessel's correction) accounts for the fact that a sample tends to underestimate population variability.