Basic Math Calculators

Basic Math Calculators - Arithmetic Done Right, Every Time

Basic math calculations underpin almost every professional and academic task. Discounts, percentages, averages, ratios, fractions - these appear constantly in finance, science, engineering, cooking, and everyday decision-making. These calculators eliminate arithmetic errors and, more importantly, show the formula so you understand the method.

Thirty Basic Math Calculators

Percentage Calculator - Three modes: (1) what is X% of Y? (2) X is what percent of Y? (3) percentage change from X to Y. The most versatile math calculator on the site - used for discount calculations, exam marks, profit/loss percentages, and population growth rates.

Percentage Change Calculator - Dedicated tool for calculating the percentage increase or decrease between any two values. Enter an old value and a new value to instantly see the percentage change (with sign), direction (increase or decrease), and absolute difference. Handles negative starting values correctly. Essential for tracking stock returns, salary hikes, weight loss, electricity bill changes, and any before/after comparison.

Percentage Increase Calculator - Three modes: (1) find % increase from old to new value, (2) find the new value after a given % increase, (3) find the original value from a post-increase amount. Handles salary hikes, markup pricing, population growth, and any scenario where values go up.

Percentage Increase Classic - The pure classic formula: enter old value and new value, instantly get the percentage increase, absolute increase, and growth multiplier. Single-mode, no reverse calculations. Ideal for students learning the textbook formula or anyone who needs a clean, direct percentage increase result.

Decimal to Percent Converter - Two-direction converter: enter a decimal (like 0.75) to get 75%, or enter a percentage (like 75) to get 0.75. Shows fraction form and ratio alongside the converted value. Handles values over 1.0 (produces percentages over 100%), very small decimals, and negative values.

Percentage Decrease Calculator - Three modes: (1) find % decrease from old to new value, (2) find the new value after a given % decrease, (3) find the original price before a discount was applied. Handles sales, cost reductions, weight loss, and any scenario where values fall.

Percentage Difference Calculator - Symmetric comparison of two values with no reference direction. Uses the average of both values as the denominator, so swapping V1 and V2 gives the same result. Correct for comparing two independent measurements, two prices, or two survey results from the same time period.

Weighted Average Calculator - Calculate weighted mean for any list of values and weights entered as comma-separated lists. Includes a CGPA mode for Indian university grading (O, A+, A, B+, B, C, P, F) with credit hours. Shows per-item contribution breakdown and compares weighted average to simple average.

Mean Calculator - Compute all four classical means from one dataset: arithmetic mean, geometric mean, harmonic mean, and quadratic mean (RMS). Also includes a Weighted Mean mode with per-value custom weights. Verifies the AM greater than or equal to GM greater than or equal to HM inequality for positive datasets.

Average Calculator - Arithmetic mean, median, and mode for any set of comma-separated numbers, plus count, sum, min, and max. Handles any dataset size.

Fraction Calculator - Add, subtract, multiply, and divide fractions with unlike denominators. Shows full working: LCM for denominator, equivalent fractions, operation, and simplification. Supports mixed numbers and improper fractions.

Square Root Calculator - √x and nth roots, plus x² and xⁿ. Flags perfect squares explicitly. Used in geometry (Pythagorean theorem, see the Pythagorean Calculator), physics, and algebra.

Ratio Calculator - Three modes: (1) simplify a ratio to lowest terms (e.g., 15:25 → 3:5), (2) find a missing value in a proportion (cross-multiplication), (3) scale a ratio to a target total (e.g., mix 3:5:2 totalling 500g). Used in recipe scaling, map reading, and financial ratio analysis.

Geometric Mean Calculator - Two modes: (1) geometric mean of any list of positive values (the nth root of their product), (2) CAGR mode - find compound annual growth rate from a start value, end value, and number of years. Shows arithmetic mean and harmonic mean alongside for the AM-GM-HM comparison.

Harmonic Mean Calculator - Two modes: (1) harmonic mean of any list of positive values (n divided by sum of reciprocals), (2) average speed mode for equal-distance round trips. Shows all three classical means (HM, GM, AM) and verifies the AM-GM-HM inequality.

Factorial Calculator - Three modes: (1) n! factorial - finds the product of all integers from 1 to n and shows the full expansion for n up to 15; (2) nPr permutation - counts ordered arrangements of r items chosen from n; (3) nCr combination - counts unordered selections of r items from n. Supports values from 0 to 170 with scientific notation for large results.

GCF and LCM Calculator - Calculate both the greatest common factor AND least common multiple of 2 to 8 numbers simultaneously. Shows prime factorizations, the Euclidean algorithm for GCF, the prime factor method for LCM, and verifies the identity GCF × LCM = a × b for two-number inputs. Use when you need both values at once.

GCF Calculator - Find the greatest common factor (GCF/GCD/HCF) of 2 to 8 numbers. Shows the step-by-step Euclidean algorithm, prime factorization of each input, and the LCM as a secondary result. Supports integers up to 1 billion.

LCM Calculator - Find the least common multiple of 2 to 8 numbers using the GCF-division method. Shows step-by-step arithmetic, prime factorizations, and GCF as a secondary result. Essential for adding fractions and solving scheduling problems.

Relatively Prime Calculator - Check whether two integers are coprime (relatively prime) by computing their GCF with the Euclidean algorithm. Shows the full step-by-step algorithm, prime factorizations of both numbers in exponent notation, and a complete list of all common divisors. Returns Yes when GCF = 1, No otherwise.

Prime Factorization Calculator - Decomposes any integer up to 10 million into prime factors using trial division, displays the result in exponential notation (e.g., 360 = 2³ × 3² × 5), shows whether the number is prime, and counts total divisors. Includes a separate GCF and LCM calculator for any two numbers.

Root Mean Square Calculator - Two modes: (1) RMS (quadratic mean) for any list of values - shows mean, standard deviation, sum of squares, and the identity RMS² = Mean² + Variance, (2) AC voltage mode - find RMS voltage from peak voltage for sinusoidal signals, with form factor and average voltage.

Average Percentage Calculator - Two modes: (1) simple (arithmetic) average of a list of percentages, showing min, max, sum, and range, (2) weighted average of percentages using group sizes as weights - the correct method when groups have different populations. Shows how much the weighted result differs from the simple average.

Percent Error Calculator - Compute the percentage error between an experimental (measured) value and the true (accepted) value. Shows absolute error, signed error (over/underestimate direction), and a plain-language interpretation. Essential for chemistry lab reports, physics experiments, and quality control accuracy assessment.

Percentage Point Calculator - Distinguish between a percentage point change and a percentage change. Two modes: (1) find the pp difference between two percentages, (2) find the new percentage after a pp change. Includes basis point conversion (1 pp = 100 bp). Critical for correctly interpreting interest rate and polling data changes.

Doubling Time Calculator - Find the time for any value to double at a given growth rate. Two modes: (1) exact formula using compounding frequency (annual, semi-annual, quarterly, monthly, or continuous), (2) Rule of 72 approximation with comparison to Rule of 70. Shows error between approximation and exact value.

Prime Number Calculator - Two modes: (1) check if any integer up to 10,000,000 is prime or composite, with next prime, previous prime, and smallest factor; (2) list all prime numbers up to a given limit (up to 10,000) with count and sum. Uses trial division for speed.

Standard Form Calculator - Two-mode converter for standard form (scientific notation). Mode 1 converts any real number into A times 10 to the n notation, showing the coefficient and exponent separately. Mode 2 converts from standard form back to a full decimal number. Handles very large numbers (astronomical distances) and very small numbers (sub-atomic scales) with equal precision.

Slope Percentage Calculator - Convert between three slope representations: rise/run ratio, angle in degrees, and percent grade. Three input modes. Outputs grade percentage, angle, 1:n ratio, and a category label (Flat through Extreme). Used for road grades, ramp design, roof pitch, and terrain analysis.

Time Percentage Calculator - Two modes: (1) convert any duration (hours and minutes) to a percentage of a chosen period - day, week, month, or year; (2) find the duration that equals a given percentage of a period. Used for work-hour tracking, project time allocation, and shift scheduling.

Percentage of a Percentage Calculator - Two modes: (1) Product - find P1% of P2% (e.g., 30% of 25% = 7.5%) with combined probability and effective remaining; (2) Sequential - compute the net effect of two back-to-back percentage changes with the interaction term that explains why sequential changes don’t simply add. Essential for stacked discounts, compound growth, and joint probability.

When Basic Math Gets Tricky

The most common error in percentage calculations is confusing percentage points and percentages - if interest rates rise from 4% to 6%, that is a 2 percentage-point increase but a 50% increase in rate. The Percentage Calculator handles both interpretations correctly. For tracking change between two specific values (before and after), the dedicated Percentage Change Calculator is faster and shows the direction explicitly. When you need only increases, use the Percentage Increase Calculator; for reductions and discounts, use the Percentage Decrease Calculator.

When comparing two values with no reference direction (two competing prices, two lab measurements, two survey results from the same period), the Percentage Difference Calculator is the correct tool - it is symmetric and has no implied “before” or “after.” For data analysis, the Average Calculator and Weighted Average Calculator handle unweighted and weighted datasets respectively.

The Geometric Mean Calculator is the correct average for growth rates and investment returns - it directly computes CAGR from start and end values. For rates and speeds, the Harmonic Mean Calculator gives the true average (for example, average speed over equal distances). For AC circuits, signal processing, or error analysis, the Root Mean Square Calculator computes the quadratic mean. When you need the building blocks of a number, the Prime Factorization Calculator decomposes it into primes and finds GCF and LCM. For averaging percentages correctly (especially when groups have unequal sizes), the Average Percentage Calculator applies proper weighting. For deeper statistics, see the Standard Deviation Calculator.