Mathematics Tools
Calculators that compute exactly, true fractions, arbitrary-precision integers, simplified radicals, and show their working step by step. No floating-point rounding, no "0.9999999999", and nothing you type leaves your browser.
- Fraction Calculator 1 1/2 + 3/4 = 9/4 = 2 1/4, exactly, with the steps shown. Fractions, mixed numbers and decimals in; simplified fraction, mixed number and decimal out.
- Decimal ⇄ Fraction Converter 0.625 = 5/8, and 0.1666… = 1/6 exactly. This converter handles repeating decimals properly in both directions, showing the repetend in parentheses.
- GCD & LCM Calculator GCD(48, 180, 36) = 12 and LCM = 720, for any list of numbers, any size, with the Euclidean algorithm written out step by step.
- Prime Factorizer & Prime Checker Is 1,000,000,007 prime? (Yes.) What is 360 as a product of primes? (2³ × 3² × 5.) Exact answers up to 19-digit numbers, plus divisor counts.
- Ratio Calculator If 3 : 4 = 9 : x, then x = 12, solved exactly by cross-multiplication, with fractions kept as fractions. Plus one-click ratio simplification (48 : 36 = 4 : 3).
- Quadratic Equation Solver x² − 3x − 10 = 0 → x = 5 or x = −2, exactly, and when roots aren't rational you get the simplified radical form (3 ± √89)/2, not just a decimal.
- Statistics Calculator Paste your numbers, get the full descriptive-statistics table: mean, median, mode, quartiles, IQR, and both flavors of variance and standard deviation, with the sample/population distinction made explicit.
- Roman Numeral Converter 2026 = MMXXVI. Type in either box and the other updates, with proper validation, so "IIII" and "IC" are flagged with their canonical spellings instead of silently accepted.
- Scientific Notation Converter 299,792,458 = 2.99792458 × 10⁸, converted on the digits themselves, so a 21-digit number keeps all 21 digits instead of being rounded by floating point.
- Permutations & Combinations Calculator How many 5-card poker hands? C(52, 5) = 2,598,960, exactly. Combinations, permutations and factorials with arbitrary-precision integers, formulas shown.
- Long Division Calculator (with Steps) 7439 ÷ 12 = 619 r 11, with every bring-down step laid out the way it's taught, plus the exact decimal (619.91(6), repetend in parentheses).
- Radical Simplifier & Surd Calculator √180 = 6√5, via the prime factorization, shown. Plus rationalizing c/(a + b√m) with the conjugate, and combining like surds (3√8 + 5√18 = 21√2).
- Modular Arithmetic Calculator 7¹²⁸ mod 13 in seven squarings, not 128 multiplications, with the square-and-multiply table shown. Plus modular inverses (17⁻¹ mod 43) via extended Euclid, step by step.
- Slope & Line Equation Calculator Through (1, 2) and (4, 4): slope m = 2/3 exactly, y-intercept b = 4/3, and the line in all three forms, slope-intercept, point-slope and integer standard form.
- Distance & Midpoint Calculator From (−2, 1) to (4, 5): distance = 2√13 exactly, the simplified radical form homework requires, with the decimal alongside, and the midpoint (1, 3).
- Binomial Expansion Calculator (2x − 3)⁴ = 16x⁴ − 96x³ + 216x² − 216x + 81, expanded with exact BigInt coefficients, plus the k-th term on demand and Pascal's row for n.
- Significant Figures Calculator 0.004560 has 4 significant figures, and this calculator shows you exactly which digits count and why, digit by digit, then rounds to any precision you need.
- Degrees ⇄ Radians Converter 45° = π/4, not 0.7853981634. Exact π-fraction conversion both ways, plus a degrees-minutes-seconds panel for GPS-style coordinates.
- Completing the Square Calculator 2x² − 4x + 5 = 2(x − 1)² + 3, completed exactly, with the halve-and-square working written out, plus the vertex (1, 3) it hands you for free.
- Synthetic & Polynomial Long Division (x³ − 6x² + 11x − 6) ÷ (x − 2) = x² − 4x + 3, remainder 0, so (x − 2) is a factor. The classic synthetic tableau, drawn for your numbers, plus full long division for any divisor.
- Percentile Calculator P40 of your data, three ways at once: linear interpolation (Excel's PERCENTILE.INC), nearest rank, and exclusive interpolation (PERCENTILE.EXC), because they genuinely disagree, and knowing which one your course or spreadsheet uses is the whole game.
- Divisibility Rules Checker Is 123456 divisible by 8? By 11? Every rule from 2 to 13 applied with its working shown, digit sums, last-digits checks, the truncate-and-double trick for 7, so you learn the rule while getting the answer.
- Weighted Average Calculator Three exam scores at 20%, 30% and 50% weight, the exact course grade, with the multiply-add-divide working shown, and weights that don't need to total 100.
- Exponent Calculator 2^100 = 1,267,650,600,228,229,401,496,703,205,376, every digit, where ordinary calculators overflow to 1.2676506e30. Negative and fractional exponents come out exact too.
- Circle Calculator (in Terms of π) r = 6 → area = 36π, circumference = 12π, the "in terms of π" form the homework asks for, plus arc length and sector area for any central angle, exact.
- Triangle Area Calculator (Heron's Formula) Sides 3, 5, 6 → area = 2√14 exactly, via Heron's formula in its integer-safe form, with the triangle inequality checked and every step shown.
- Triangle Solver (Law of Sines & Cosines) Enter any three values (with at least one side) and get the complete triangle, all sides, all angles, area and perimeter, drawn to scale.
- Matrix Calculator Enter one or two matrices and compute the determinant, inverse, transpose, sum, difference or product, for 2×2 and 3×3.
- Logarithm Calculator Find log base b of any value, or ln, log₁₀ and log₂ at once, and reverse it with the antilogarithm.
- Arithmetic & Geometric Sequence Calculator Enter the first term, the common difference or ratio, and how many terms to get the nth term, the sum and the sequence itself.
- Vector Calculator (2D & 3D) Enter two 2D or 3D vectors to get their magnitudes, sum, difference, dot and cross products, and the angle between them.
Exact math, with the steps
Most calculators quietly round; these don't. Fractions are added and simplified exactly with the steps shown, repeating decimals convert back to exact fractions, primality uses Miller, Rabin, quadratics keep radical roots, and combinatorics and exponents run at BigInt scale, so 2¹⁰⁰ is digit-for-digit correct. Where a topic has a method, long division, synthetic division, completing the square, the working is laid out, not hidden.
That makes these useful for learning as well as answers, and it all runs in your browser: private, instant and offline. For applied number-crunching see Calculators, Statistics and Finance.
Frequently asked questions
What makes these different from other math calculator sites?
Exactness. These tools compute with arbitrary-precision integers and true rational arithmetic, fractions stay fractions, roots come out in simplified radical form like (3 + √89)/2, and 1000! is produced digit-perfect. Ordinary calculators (and spreadsheet formulas) work in floating point, which silently rounds past 15-17 significant digits and turns 1/3 + 2/3 into 0.9999999999999999.
Why not just ask an AI chatbot?
Language models are notoriously unreliable at arithmetic. They generate plausible-looking numbers rather than computing them, and you can't tell a right answer from a confident wrong one. These calculators run the actual algorithms (Euclid, Miller, Rabin, the quadratic formula) and show the working, so the answer is checkable, not just believable.
Do the tools show the steps?
Where steps are the point, yes, the fraction calculator shows the common-denominator working, the GCD calculator writes out the Euclidean algorithm line by line, and the quadratic solver walks from discriminant to simplified roots. The answer alone teaches nothing; the working is what you check homework against.
Do they work offline?
Yes, every computation runs in your browser with no server involved, so once a page has loaded it works with the connection off.