Numbers & arithmetic
Number theory and base conversion: primes, divisors, GCD and LCM, roman numerals, binary and hexadecimal. 58 tools, including Calculator, Amicable Number Checker, Arctan2 Calculator (atan2 of y and x) and Carry and borrow visualizer. All free, with no account and nothing to install.
CalculatorEvaluate math expressions with parentheses, powers and modulo, live.Amicable Number CheckerCheck whether two numbers are amicable — or give just one and get its candidate partner plus the verified loop, with perfect and sociable numbers identified.Arctan2 Calculator (atan2 of y and x)atan2(y, x) is not atan(y/x): it reads the signs of both arguments to place the angle in the right quadrant over the full −180°…180° turn, and it stays defined when x = 0. Enter x and y, read the angle in degrees or radians, see the quadrant and the point plotted. For a single ratio with no quadrant information, use the arctan calculator instead.Carry and borrow visualizerAdds or subtracts two whole numbers the way it is taught in school — set up in columns, digit by digit — and highlights every carry (addition) or borrow (subtraction) as it happens. A clear way to see the mechanic behind column arithmetic.Ceiling and floor function calculatorThe ceiling ⌈x⌉ rounds up to the next integer, the floor ⌊x⌋ rounds down. Enter any number to get both, plus the ordinary round, the truncation toward zero and the fractional part left over.Common Factor CalculatorFind every common factor of 2 to 10 numbers, with the greatest common factor highlighted and coprime pairs flagged.Comparing fractions calculatorWhich fraction is bigger? Enter two and it cross-multiplies to compare them exactly — no rounding — and shows both as decimals so you can see how close they are.Continued fraction calculatorExpand a number into its continued fraction [a₀; a₁, a₂, …] and list the convergents — the best rational approximations at each step. Feed it a decimal, an exact fraction a/b, or a square root √k: rationals terminate, √k is periodic, and irrationals stream on to the term cap. Continued fractions give the closest fractions for a given size of denominator and reveal the hidden structure of numbers like the golden ratio and π.Cube calculatorCompute the volume and surface area of a cube from its side length.Decimal to fraction calculatorConvert a decimal number into a simplified fraction.Digit sum calculatorAdd up the digits of a number and find its digital root.Divide into equal parts calculatorSplit an amount into a chosen number of equal parts: the exact size of each part, plus a whole-cent split — the rounded value each part gets and the small remainder to distribute so the pieces add back to the total.Divisibility Test CalculatorTest a number against the divisors 2 to 12, the primes up to 100 or your own list — and see the mental rule and the working, not just yes or no.e Digits Calculator (Euler's Number)Compute up to 1,000 decimals of Euler's number e from the series Σ 1/k!, with digit frequencies, a digit search and the 1828 1828 trap explained.Egyptian fraction calculatorEvery proper fraction can be written as a sum of distinct unit fractions (1/2 + 1/3 …), the way ancient Egyptian scribes did. This runs Fibonacci's greedy algorithm and shows the decomposition.Equivalent fractions calculatorReduce a fraction to lowest terms and see a few equivalent forms built by multiplying up, plus its decimal and percentage — everything that names the same value a different way.Estimation calculator (rounding)The mental-maths trick, made explicit: round each number to one significant figure, do the operation, and compare the quick estimate with the exact answer and the error it carries.Euler characteristic calculator (V − E + F)For a polyhedron or a triangulated surface, χ = V − E + F. A convex polyhedron gives χ = 2; the genus g = (2 − χ)/2 tells you how many handles the surface has (0 = sphere, 1 = torus).Euler's totient calculator φ(n)Compute Euler's totient φ(n) — the count of integers from 1 to n that are coprime to n (share no factor but 1). It factorises n into primes and applies φ(n) = n·∏(1−1/p) over its distinct prime factors, showing the factorization, the formula and the number of coprimes. φ underlies RSA, Euler's theorem and the order of the multiplicative group mod n.Even or Odd CheckerPaste a whole list of numbers and get each one classified even or odd, with the counts and the parity rule explained — including 0 and negative numbers.Extended Euclidean algorithm calculatorRun the extended Euclidean algorithm on two integers a and b: it returns their greatest common divisor together with Bézout coefficients x and y satisfying a·x + b·y = gcd(a, b). Beyond the gcd, those coefficients are exactly what you need to build modular inverses and solve linear Diophantine equations. The full division step table is shown so you can follow every reduction.Factor CalculatorList every divisor of a whole number in pairs, with the divisor count, the divisor sum, and whether it is prime, perfect, abundant or deficient.Find minimum and maximumPaste a list of numbers and get the smallest, the largest, the range between them, and how many values there are. Handles negatives and decimals.First n prime numbersList the first n prime numbers — the building blocks of arithmetic that have no divisors but 1 and themselves. Enter how many you want (up to 10,000) and it returns the sequence, the nth prime itself and the sum of them all.Fraction CalculatorAdd, subtract, multiply or divide two fractions and get the reduced result plus its decimal value.Gacha pity calculatorHow many pulls until the guaranteed 5★ in a gacha game like Genshin or Star Rail, accounting for the soft-pity ramp. Enter your current pity count and it works out the pulls left to soft pity, the hard-pity guarantee, and the average pulls you can expect before the next drop.Goldbach conjecture verifierGoldbach's conjecture says every even number above 2 is the sum of two primes. Enter an even number and it finds such a pair (the one with the smallest first prime), confirming the conjecture for that value.Greatest Common Factor CalculatorFind the GCF of up to 15 numbers with three methods side by side: the Euclidean algorithm, prime factorisation and factor listing.LCM calculatorFind the least common multiple (and GCD) of two numbers.List of prime numbersList every prime number up to a chosen limit, using the Sieve of Eratosthenes. Enter an upper bound (up to 100,000) and it returns all primes at or below it, how many there are and their sum — a quick reference for factoring and number theory.Log Base 10 CalculatorCompute log₁₀(x) for a single value, a whole list at once, or invert it to find x from a known logarithm.Log Base 2 CalculatorCompute log₂(x) for any positive number, with exact results flagged for powers of two.Long Division CalculatorDivide two whole numbers to get the quotient, remainder and exact decimal result.Mersenne Prime CheckerRun the Lucas-Lehmer test on 2^p - 1 for any exponent p up to 5000, with the digit count, the rank in the known list and the even perfect number it generates.Modular multiplicative inverse calculatorFind a⁻¹ mod m — the number x with a·x ≡ 1 (mod m) — using the extended Euclidean algorithm. An inverse exists exactly when gcd(a, m) = 1; otherwise the tool reports that none exists. The modular inverse is what lets you 'divide' in modular arithmetic and is the step that produces the RSA private exponent d from the public exponent e.Modulo calculatorCompute the remainder and quotient of a division (modulo).Multiple fraction calculatorAdd, subtract, multiply or divide any number of fractions in one go — not just two. Enter as many numerator/denominator rows as you like, pick the operation, and it chains them left to right and reduces the answer to lowest terms, with the decimal and mixed-number forms.Number of Digits CalculatorCount the digits of any integer in any base from 2 to 36, with the digit sum, product, first and last digit, and palindrome and repdigit flags.Number Pattern FinderFind the rule behind a sequence: arithmetic, geometric, quadratic, cubic, Fibonacci, powers, triangular, factorial, primes or a linear recurrence, with the difference table and the next terms.Optimization calculator (calculus)Find the minima and maxima of a function on an interval — the heart of every optimization problem. Enter f(x) and a range; it differentiates symbolically, locates the critical points where f′(x)=0, classifies each with the second derivative, and reports the global minimum and maximum on the interval.Order of Operations Calculator (PEMDAS)See why order matters: compute a + b × c the correct (PEMDAS) way versus naive left-to-right.Pi Digits CalculatorCompute up to 10,000 decimals of π live in your browser, search any digit string, see the digit frequencies and the Feynman point.Prime Factor CalculatorFactor any integer up to 10^15 with Pollard's rho and Miller-Rabin, with the factor tree, exponent form, divisor count, sigma and Euler's totient.Prime factorization calculatorBreak a whole number down into the product of its prime factors.Prime number checkerCheck whether a number is prime and find its smallest divisor.Product notation calculator (pi notation)Evaluate a product ∏ f(n) from a lower to an upper index — the multiplicative sibling of summation. Type any expression in n, set the bounds, and it computes the exact product with a term-by-term breakdown. Great for factorials, Wallis-type products and telescoping products.Roman Numeral Math SolverAdd, subtract, multiply or divide Roman numerals (or Arabic 1–3999): parse each value, show the Arabic working and format the result back to a Roman numeral, with division quotient and remainder.Rounding calculatorRound a number to a chosen number of decimal places.RSA encryption simulatorWalk through the RSA public-key cryptosystem end to end with your own primes. Enter two primes p and q and a numeric message m: the simulator computes the modulus n = pq and the totient φ = (p−1)(q−1), picks or validates a public exponent e coprime to φ, derives the private exponent d = e⁻¹ mod φ, then encrypts c = mᵉ mod n and decrypts back mᵈ… = m — every step shown with big-integer arithmetic. The definitive way to see why RSA actually works.Scientific CalculatorFull scientific calculator with trigonometry (DEG/RAD), logarithms, powers, memory and history.Scientific notation converterConvert a number into scientific notation (mantissa × 10ⁿ).Sigma notation calculator (summation)Evaluate a summation ∑ f(n) from a lower to an upper index. Type any expression in n — powers, fractions, factorials, trig, exponentials — set the bounds, and it computes the exact sum plus a term-by-term breakdown, live as you type.Significant figures calculatorRound a number to a chosen number of significant figures.Soroban abacus simulatorAn interactive Japanese soroban you can actually use. Click the beads across thirteen columns — one heaven bead worth five and four earth beads worth one each — and the decimal value updates live beneath. Clear it, roll a random number, type a value to set the beads, or solve a quick addition, subtraction, multiplication or division and show the answer on the frame.Sum calculatorAdd up a list of numbers and get the total, count and average.Sum of cubes calculatorAdd up cubes fast: the sum of the first n cubes (1³+2³+…+n³, which equals the square of the n-th triangular number), the cubes over a range n₁³…n₂³, or the cubes of your own list of numbers. Exact integer arithmetic, however large.Sum of positive integers calculatorThe sum of all whole numbers from n₁ to n₂ in one step — Gauss's trick, n₂(n₂+1)/2 − (n₁−1)n₁/2, instead of adding them one by one. From 1 to 100 is the classic 5050; works for any range and any size.Twin prime finderFind every pair of twin primes up to a limit — primes that differ by exactly 2, like (11, 13) or (17, 19). Enter an upper bound (up to 1,000,000) and it lists the pairs and counts them. Whether infinitely many exist is one of the oldest open problems in mathematics.