Mathe-Rechner
Rechner für Schule, Beruf und Alltagsmathematik. Berechnen Sie Prozente und Brüche, lösen Sie lineare und quadratische Gleichungen, bestimmen Sie Seiten und Winkel eines Dreiecks oder Mittelwert, Standardabweichung und Wahrscheinlichkeit einer Zahlenreihe.
Wo es hilft, wird der Rechenweg Schritt für Schritt gezeigt, damit Sie die Methode nachvollziehen und Ihr eigenes Ergebnis prüfen können.
Arithmetic and fractions Alle ansehen
Decimal to Fraction CalculatorTurn a decimal into a fraction in lowest terms, including repeating decimals such as 0.333.Scientific CalculatorType a whole calculation with brackets, powers, roots, logs and trigonometry, and see the answer as you type.Long Division CalculatorDivide any two numbers and see the quotient, the remainder, the decimal answer and every step of the working.Exponent CalculatorRaise any number to a power, including negative, decimal and fraction exponents, with exact answers for whole numbers.Logarithm CalculatorWork out a logarithm to any base, find the natural log, the log to base 10 and base 2, or reverse it to find an antilog.Scientific Notation CalculatorConvert a number to scientific notation (standard form), engineering notation and E notation, or turn it back into a plain number.Factorial CalculatorWork out n factorial exactly, even for large numbers, with the digit count, trailing zeros and the double factorial.Square Root and Nth Root CalculatorFind the square root, cube root or any other root of a number, in simplest radical form, with a check for perfect powers.Rounding and Significant Figures CalculatorRound a number to decimal places, tens and hundreds, or significant figures, using the rule you choose, and count the significant figures in it.Fraction CalculatorAdd, subtract, multiply and divide fractions, simplify them and convert to decimals, with steps.Ratio CalculatorSimplify ratios, scale them up or down, solve a proportion and share a total in a ratio.
Percentages Alle ansehen
Percentage CalculatorWork out percentages, percentage change and increases or decreases.Reverse Percentage CalculatorFind the original price or amount before a percentage increase or decrease was applied.Percentage Point CalculatorFind the difference between two percentages in percentage points, and compare it with the percentage change.Percentage Difference and Percent Error CalculatorFind the percentage difference between two values, or the percent error of a measurement against the true value.
Algebra Alle ansehen
Quadratic Equation SolverSolve ax² + bx + c = 0 with the quadratic formula, with the discriminant, exact roots, the vertex and the working.Linear Equation SolverSolve a linear equation such as 3x + 4 = x + 10 for x, with every step and an exact fraction answer.Simultaneous Equations SolverSolve two equations with two unknowns, or three equations with three, with exact answers and a check for no solution.Cubic Equation SolverSolve ax³ + bx² + cx + d = 0 for all three roots, real and complex, with exact roots when they are rational.Matrix CalculatorAdd, subtract and multiply matrices up to 4 by 4, and find a determinant, inverse, transpose, trace, rank or power, with exact fractions.Vector CalculatorAdd and subtract vectors, and find the dot product, cross product, magnitude, angle, unit vector and projection.Arithmetic Sequence CalculatorFind any term and the sum of an arithmetic sequence, or work out the first term and common difference from two known terms.Geometric Sequence CalculatorFind any term, the sum of the first n terms and the sum to infinity of a geometric sequence.Complex Number CalculatorAdd, subtract, multiply and divide complex numbers, and find the modulus, argument, conjugate, square root and powers.Equation of a Line and Slope CalculatorFind the equation, slope, angle, percentage grade and intercepts of a straight line from two points, a point and a slope, or a general equation.Distance and Midpoint CalculatorFind the distance between two points and their midpoint in two or three dimensions, or find the other end of a line from one end and the midpoint.
Geometry and trigonometry Alle ansehen
Pythagorean Theorem CalculatorFind the missing side of a right-angled triangle, with area, perimeter and angles.Triangle CalculatorEnter any three known values of a triangle, sides and angles, and get the rest, with the area, perimeter and the sine and cosine rule working.Arc Length CalculatorFind the length of an arc, the area of a sector, the chord and the segment from the radius and an angle.Regular Polygon CalculatorFind the area, perimeter, angles, apothem and diagonals of a regular polygon from its number of sides and one measurement.Trigonometry CalculatorFind the sine, cosine, tangent and their reciprocals of any angle with exact values, or find the angle from a sine, cosine, tangent or two sides.Area and Volume CalculatorWork out the area, perimeter, volume and surface area of common shapes in the units you choose.
Statistics and probability Alle ansehen
Standard Deviation CalculatorFind the standard deviation and variance of a list of numbers, for a sample or a whole population, with the working.Quartile CalculatorFind the quartiles, median, interquartile range and outliers of a list of numbers, using the method your course or spreadsheet uses.Permutation and Combination CalculatorWork out nPr and nCr exactly, with and without repeats, for choosing r items from n.Binomial Probability CalculatorFind the chance of exactly, at most or at least k successes in n trials, with the mean and standard deviation.Confidence Interval CalculatorFind the confidence interval for a mean from a sample, or for a proportion, with the margin of error.Sample Size CalculatorWork out how many people to survey for a proportion, or how many measurements for a mean, for the margin of error you want.Weighted Average CalculatorFind the weighted average of values that count for different amounts, such as grades with different weightings.Probability CalculatorWork out the chance of two events happening together or either happening, for independent, exclusive and dependent events, and repeated trials.Normal Distribution and Z-Score CalculatorFind z-scores, the probability of a value being below, above or between limits in a normal distribution, or the value for a given probability.Linear Regression and Correlation CalculatorFit a straight line to pairs of values and get the slope, intercept, correlation coefficient, r squared and a prediction.Average CalculatorFind the mean, median, mode, range, sum, count and standard deviation of a list of numbers.
Number theory Alle ansehen
GCD and LCM CalculatorFind the highest common factor and lowest common multiple of two or more numbers.Prime Number CheckerCheck whether numbers are prime, see their prime factors and find the next prime.Modulo CalculatorFind the remainder of a division, a power modulo a number, or the modular inverse, with correct handling of negative numbers.Fibonacci CalculatorFind any Fibonacci number exactly, list the first terms, or check whether a number is in the sequence.Factors and Prime Factorisation CalculatorList every factor of a number, see its prime factorisation with the division steps, and learn whether it is prime, square or perfect.
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Ratgeber zum Einstieg
Standard deviation explained with a worked example
Learn what standard deviation measures, how to calculate it for a population and a sample step by step, and how to read the result.
Converting between fractions, decimals and percentages
Convert between fractions, decimals and percentages with simple rules, a table of common values and worked examples for prices, recipes and test marks.
How to calculate how much paint you need for a room
Measure walls and ceilings, subtract doors and windows, allow for coats and waste, and turn the area into litres and tin sizes with a full worked example.