Mathematics & Statistics Calculators: Equations, Matrices & Regression
Choose calculators for quadratic and simultaneous equations, matrix determinants/inverses, logarithms, descriptive statistics, and linear regression.
What do you need to calculate?
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| Goal and tool | Required inputs | How to check |
|---|---|---|
| Quadratic roots and discriminant D → | Coefficients a, b and c (a ≠ 0) | Substitute roots into the original equation |
| 2×2 & 3×3 determinant det(A) and inverse A⁻¹ → | Square matrix entries (2×2 or 3×3) | Verify det(A) ≠ 0 and A × A⁻¹ = I |
| 2- and 3-variable simultaneous linear equations → | Coefficients and constant terms for each equation | Check nonzero determinant and substitute back |
| Mean, median, variance and standard deviation → | A numeric dataset with consistent conditions | Check count, outliers and N vs. N−1 denominator |
| Least-squares regression line y=ax+b and r → | Paired (x, y) observations | Review R², residuals, outliers and extrapolation |
| Common, natural and arbitrary-base logarithms → | Base a (a>0, a≠1) and argument x (x>0) | Check via change-of-base ln(x)/ln(a) |
Move equation terms to one side and check det(A) ≠ 0 for matrix inverses. For statistics, verify the N vs. N−1 denominator convention. A fitted regression does not establish causation.
19 calculators
Quadratic Equation
Solve ax² + bx + c = 0 with real or complex roots, the discriminant and substitution into the quadratic formula.
Statistics Calculator
Paste numbers to get count, sum, mean, median, min, max and standard deviation at once. Handles newline, comma and space separators.
Fraction Calculator
Add, subtract, multiply and divide fractions with exact results. See the reduced answer plus mixed-number and decimal forms, with the working shown.
Prime Factorization
Factor an integer at least 2 with up to 15 digits. Check product and exponent forms, positive divisor count and primality. Press Factorize or Enter to run.
Permutation & Combination Calculator
Compute nCr, nPr and n! with exact big-integer arithmetic. Large results such as lottery odds never overflow, and every calculation shows its working step by step.
Trigonometry Calculator
Enter an angle to get sin, cos and tan at once. Special angles like 30°, 45° and 60° are shown as exact values (1/2, √3/2), with degree and radian support, pi expressions such as pi/6, plus the quadrant signs and the reference-angle working.
Logarithm Calculator
Compute logarithms in any base, like log₂(8). One-tap bases for 2, 10 and e, with the change-of-base working (ln x ÷ ln b) and a check that bʸ returns x. Common and natural logarithm notes included.
Sequence & Series Calculator
Compute finite arithmetic and geometric terms and sums with substituted working. Supported integer inputs use exact BigInt; decimal and other paths are approximate. Check term-count and ratio limits.
Vector Calculator (Dot Product)
Compute the dot product, magnitudes and the angle between 2D or 3D vectors with fully substituted working. Includes the cosθ = (a·b) ÷ (|a||b|) step and perpendicular detection via a·b = 0 — handy for math and physics.
Matrix Determinant & Inverse
Compute the determinant and inverse of 2×2 and 3×3 matrices with cofactor-expansion working. Detects singular matrices (det = 0) and verifies the inverse — useful for math B and linear algebra students.
GCD & LCM Calculator
Compute the greatest common divisor (GCD) and least common multiple (LCM) of two or three positive integers with exact BigInt arithmetic and the Euclidean algorithm working shown.
DMS ↔ Decimal Degrees Converter
Convert angles between degrees-minutes-seconds (DMS) and decimal degrees. Useful for GPS coordinates and astronomical observations, showing the substituted formula for values like 30°45′30″ → 30.758333°.
Distance Calculator
Compute the Euclidean distance between two points in 2D or 3D with fully substituted working. Supports negative and decimal coordinates — useful for coordinate geometry and vector calculations.
Exponent Calculator
Calculate powers from a base and exponent. Safe integer bases with nonnegative integer exponents use BigInt; negative exponents and decimals are approximate. Inspect signs, scientific notation and the 0⁰ convention.
Deviation Score Calculator
Compute the deviation score from the mean, standard deviation and individual score. Shows substituted working: 50 is the mean, and a 10-point difference represents one standard deviation.
Linear Function Calculator
Find the slope a and intercept b of y = ax + b from two points, with the substituted rate-of-change formula. Useful for middle-school linear functions and trend analysis.
Complex Number Calculator
Add, subtract, multiply and divide complex numbers a + bi, with the expansion using i² = −1 and conjugate-based division shown step by step. Also shows the modulus, argument, conjugate and polar form.
Simultaneous Equation Solver
Solve systems of two or three linear equations with the elimination method shown step by step. Fractional solutions appear in exact reduced form, and inconsistent or dependent systems are detected. Ideal for checking school algebra homework.
Least Squares Regression
Paste data points to fit a least-squares regression line y = ax + b with slope a and intercept b. See the sums (Σx, Σy, Σx², Σxy), Sxx and Sxy, the correlation r, R², a scatter plot with the fitted line, residuals and predictions from x — with the working shown.
Worked examples and guides
GuideAdding and Subtracting Fractions: Steps and Visual Checks
Compare fraction operations with tables and diagrams. Learn common denominators, negative mixed numbers, zero denominators, exact checks, seven-digit inputs and rounded decimal output.
GuideGCD and LCM: Methods, Word Problems and Three Numbers
Choose GCD or LCM for reduction, denominators, cuts and repeated cycles. Includes Euclidean steps, three-number pitfalls, offset starts, trillion-size input limits and exact large results.
GuideHow to Calculate Logarithms: Rules, Change of Base and Examples
Calculate logarithms from the definition, including bases below one. Worked change-of-base examples, log vs ln, domain checks, digit-count boundaries, rounded outputs, a diagram and FAQs.
GuidePermutations vs Combinations: nPr and nCr Explained
Choose nPr or nCr by checking order, repetition and distinctness. Worked examples, a decision diagram, repeated digits, Lotto 6 odds, zero factorial and exact integer limits up to n=500.
GuideHow to Remember Trig Values: Deriving 30, 45 and 60 Degrees
Learn sin, cos and tan with two triangles and a unit circle. Exact-value tables, 150° and negative-angle signs, degree/radian inputs, undefined tan90° and practical checks.
GuideHow to Calculate Deviation Scores (T-Scores): Formula, Target Score & Percentiles
Calculate Japanese-style deviation scores T=50+10(x−μ)/σ and back-calculate target raw marks. Compare N vs. N−1 standard deviations, inspect a skewed-distribution counterexample where 50 is not the median, and check normal-model top percentile tables.
GuideHow to Use the Laws of Exponents: Product, Quotient, Power and More
Compare exponent laws, negative bases and reciprocals. Distinguish −2⁴ from (−2)⁴, understand the 0⁰ convention, fractional-exponent limits, scientific notation for 10⁻⁷ and exact versus approximate calculation.
GuideHow to Do Prime Factorization
Factor 360 with a step diagram and comparison tables. Verify product and exponent forms, derive 24 positive divisors, choose GCD/LCM or fraction tools, and check the 15-digit input limit and recalculation workflow.
GuideArithmetic and Geometric Series: How to Find the Sum of a Sequence
Compare arithmetic and geometric terms and sums with worked tables. Count terms correctly, handle r=1 and negative ratios, separate finite and infinite sums, and verify integer versus decimal calculator limits.
GuideMean, Median & Standard Deviation Guide: N vs. N−1, IQR, Outliers & Excel Comparison
Calculate mean, median, and standard deviation with a 5-score worked table. Compare population (N) vs. sample (N−1) divisors, interquartile range (IQR), CV, standard error, and Excel functions.
GuideMatrix Determinant and Inverse: 2×2 and 3×3 Worked Examples
Learn to compute the determinant and inverse of 2×2 and 3×3 matrices with fully substituted examples. Covers the 2×2 inverse formula, cofactor expansion for 3×3, why det = 0 means no inverse, and the A × A⁻¹ = I check.
GuideHow to Solve Quadratic Equations: The Formula and Discriminant
Learn to solve any quadratic equation by substituting into the quadratic formula, read the discriminant D = b² − 4ac with parabola comparison charts, and know when factoring is faster.
GuideHow to Find a Regression Line with Least Squares
Learn the least squares method step by step: build the sum table, compute Sxx and Sxy, find the slope a and intercept b, and read r and R² correctly. Includes worked examples, residuals, extrapolation and outlier cautions, and a free browser calculator for checking by hand.
GuideHow to Find the Dot Product of Two Vectors: Components and Angle
Learn the two formulas for the dot product — a·b = a₁b₁ + a₂b₂ and a·b = |a||b|cosθ — when to use each, how to find the angle between vectors, and what the sign tells you. Worked examples in 2D and 3D, plus a free browser tool.
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