Math
1,470 math calculators: percentages, fractions, equations, geometry, trigonometry, statistics and number theory. Each one shows the method in plain words, so you get the answer and understand how it was reached, free in your browser.
Exponential equation same-base solver
Solve equations like 8^(x+1) = 4^(2x−1) without logarithms: 8 becomes 2³, 4 becomes 2², the exponents are set equal and the answer is 5.
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Function zeros calculator
Enter up to four coefficients and get the points where the graph meets the x-axis: x² − 5x + 6 has the real zeros 2 and 3.
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Hyperbolic functions calculator
At 1.5 you get a hyperbolic sine of 2.12927945509, a cosine of 2.35240961524 and a tangent of 0.905148253645, all three from the same number.
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Imaginary unit powers
i to the 7th is -i, and i to the 437th is simply i: the powers of i repeat every four steps, so any whole exponent, huge or negative, lands on 1, i, -1 or -i.
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Improper fraction to mixed number converter
Eleven fourths is 2 and 3/4. Enter the numerator and the denominator to get the whole part and the leftover fraction, already reduced, so 10/4 comes out as 2…
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Inscribed angle calculator
An arc of 120 degrees gives an inscribed angle of 60, exactly half, and you also get it in radians, 1.047197551197.
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Common Difference Calculator
In 4, 9, 14, 19, 24 every step is 5, so the common difference is 5 and the sequence is arithmetic.
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Arithmetic mean calculator
The average of 2, 4, 6 and 8 is 5: their sum is 20 and there are 4 numbers. Enter any list of numbers to get the arithmetic mean together with the sum and…
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Distance between complex numbers calculator
3 + 4i is 5 units from the origin, and 1 + 2i is 5 units from 4 + 6i: enter two complex numbers and get the distance between them, the squared distance and…
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Complex number from modulus and argument calculator
A modulus of 5 at an angle of 53.130102354156° gives 3 + 4i: enter the distance from the origin and the direction, in radians or degrees, and get the real and…
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Exponential function from two points
Give two points and get the exponential function through them: (0, 3) and (1, 6) give a starting value of 3 and a base of 2, so the model is 3 · 2ˣ and it…
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Matrix scalar multiplication calculator
Multiply a 2 × 3 matrix by −2 and every entry scales at once: 1 becomes −2, 4 becomes −8 and 8 becomes −16, while the shape stays 2 × 3. Free in your browser.
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Sequence Term from Explicit Formula Calculator
Get any term of a sequence straight from its rule: 3n^2 - 2n + 5 at index 4 gives 45, with no table of earlier terms to build.
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Sum of first n even numbers calculator
The first 5 even numbers, 2 + 4 + 6 + 8 + 10, add up to 30, because the sum of the first n even numbers is n(n + 1).
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Integer checker
42 is a whole number, 3.0 counts too because its value is three, and 3.0000001 does not. Type any value and get a strict yes or no, while nonsense like abc is…
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Integration by completing the square
The integral of 1 over x² + 2x + 5 is 0.5 times the arctangent of (2x + 2)/4, plus C. Enter the three coefficients of the quadratic and see each step: the…
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Binomial expansion specific term calculator
The third term of (2x − 3y)^5 is 720x^3y^2: enter the power, the position and the two multipliers and get that single term without writing out the whole…
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Identity matrix generator
Choose the order n and get the exact identity matrix: for order 3, three ones on the diagonal and six zeros elsewhere.
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2×2 matrix inverse calculator
For rows 4, 7 and 2, 6, the determinant is 10, the adjugate has rows 6, −7 and −2, 4, and dividing by 10 gives the inverse 0.6, −0.7, −0.2, 0.4.
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Row echelon form calculator
Enter rows 1, 2, 1; 2, 1, −1; −1, 1, 2 and get a staircase with two pivots and a final row of zeros, so the rank is 2.
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Interior and exterior triangle angles calculator
Two angles of 60° and 80° leave 40° for the third, and the exterior angles come out as 120°, 100° and 140°.
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Interval notation converter
A lower bound of -2 that is included and an upper bound of 5 that is not give [-2, 5): every number from minus two up to, but not including, five.
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Absolute value equation two solutions calculator
|2x − 3| = 5 splits into 2x − 3 = 5, which gives 4, and 2x − 3 = −5, which gives −1. Enter your three numbers to see both case equations and their roots in…
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Compound rule of three calculator
If 8 workers in 6 days at 5 hours a day make 240 pieces, 12 workers in 4 days at 6 hours make 288: enter the known value and each quantity, direct or inverse…
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Collinear points checker
(0, 0), (1, 2) and (2, 4) lie on one line with slope 2: enter three points and see whether they are collinear, with the triangle area, the shared slope or a…
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Linear combination of two numbers
Find whole numbers to multiply 15 and 25 by so the sum is 10: 15 × 4 + 25 × (−2) = 10, possible because their greatest common divisor, 5, divides 10.
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Nested absolute value equation solver
||2x - 1| + 3| = 5 has two roots, -1/2 and 3/2: the solver peels the outer absolute value first, keeps only the inner value 2 because -8 is impossible, then…
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Direct proportion calculator
From one known pair, get the constant and the answer you need: if 5 gives 12, the constant is 2.4 and 8 gives 19.2.
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Data range calculator
For 12, 7, 19, 4 and 15 the range is 15: the largest value, 19, minus the smallest, 4. You also see how many values were read, which makes it quick to compare a…
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Decile calculator
Nine cut points split your data into ten equal portions: D1 marks the lowest 10 %, D5 sits at the median and D9 at 90 %.
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Excess kurtosis calculator
The values 1, 2, 3, 4 and 5 give an excess kurtosis of −1.3, flatter than the normal reference at 0.
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Grubbs outlier test calculator
Check whether one value sits suspiciously far from the rest: in 10, 11, 10, 12 and 50, the candidate is 50, set against a mean of 18.6 and the sample standard…
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Midhinge calculator
A first quartile of 5 and a third quartile of 13 give a midhinge of 9, the midpoint of the middle half of your data.
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Coefficient of determination calculator
Observed values of 3, 5, 7 and 9 against predictions that each miss by half a unit give an R squared of 0.95, with a residual sum of squares of 1 out of a total…
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Deviation scores calculator
In a set whose mean is 9, the value 4 scores −5, 7 scores −2 and 10 scores 1: the sign tells you above or below the average, the size tells you by how much.
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Geometric standard deviation calculator
Measure spread as a multiplying factor rather than a distance: a geometric standard deviation of 2 means values typically vary by a factor of two, and 1 means…
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Sturges' Rule Bin Count Calculator
A sample of 100 observations gets 8 histogram bins: one plus the base-2 logarithm of 100, rounded up.
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Cramer's V calculator
A 2×2 table of 100 observations with a chi-square of 4 gives a Cramer's V of 0.2. Near 0 means the variables barely depart from independence, near 1 means a…
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Polynomial regression calculator
Fitting degree 2 to five points from x of −2 to 2 returns the coefficients 1, 2 and 3, that is, the curve 1 + 2x + 3x².
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Regression residuals calculator
With x of 1 to 5 and y of 2, 4, 5, 4, 5, the fitted line is 2.2 + 0.6x and the third point lies 1 above it.
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Kendall's W concordance calculator for ranked data
See how closely a panel agrees on a ranking: three raters ordering four items, two identically and one swapping the top two, give a Kendall's W of…
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Total sum of squares calculator
Measure the overall spread of a data set around its mean: for 2, 4, 6 and 8 the mean is 5 and the total sum of squares is 20.
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Conditional expectation calculator
If the values 10 and 20 carry probabilities 0.2 and 0.3 inside an event, and 40 with 0.5 falls outside it, the expected value given the event is 16.
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Joint probability of two events calculator
See how likely two independent events are to happen together: probabilities of 0.6 and 0.25 multiply to 0.15.
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Poker hand probability calculator
A full house comes up in 3,744 of the 2,598,960 possible five-card hands, exactly 6/4165. Pick any category from high card to royal flush and get the exact…
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Binomial At Most Probability Calculator
For 10 trials with a 0.5 chance each and a limit of 4, the calculator adds the chances of 0, 1, 2, 3 and 4 successes into one cumulative probability.
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Geometric PMF calculator
Find the chance that the first success lands exactly on trial k: with a 0.25 chance per try, a first success on the third try has probability 0.140625, after…
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Probability Exactly One Event Calculator
If P(A) is 0.6, P(B) is 0.5 and both happen with probability 0.2, the chance that exactly one occurs is 0.7.
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Chi-Square Critical Value Calculator
With 10 degrees of freedom and a 0.05 significance level, the upper-tail critical value is 18.3070380532751.
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Discrete uniform mean and variance calculator
A fair die from 1 to 6 has 6 equally likely outcomes, a mean of 3.5 and a variance of 35/12. Enter the lowest and highest whole number, both included, and get…
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Normal probability between values calculator
Between 85 and 115 on a normal curve with mean 100 and standard deviation 15 lies just over two thirds of the probability, because each bound sits 1 standard…
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Z-score to percentile calculator
Turn a z-score into the share of a standard normal distribution at or below it: 1.96 gives a percentile of 97.50021 and 0 gives exactly 50.
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Confidence Interval for the Difference of Proportions Calculator
A rate of 0.62 in a sample of 200 against 0.51 in a sample of 180 gives a gap of 0.11, and its 95 percent interval stays above zero.
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F Distribution CDF Calculator
Enter an F statistic of 2.5 with 5 and 10 degrees of freedom and get the left-tail probability, the share of the F distribution at or below 2.5.
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Lognormal Distribution CDF Calculator
Find the chance that a positive, right-skewed quantity stays at or below a cutoff: with mu of 0 and sigma of 1 on the log scale, a value up to 2 has probability…
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Confidence Interval for a Ratio of Variances Calculator
Sample variances of 25 and 16 from 20 and 24 observations give a ratio of 1.5625, and the 95 percent interval around it includes 1.
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Sample Size for a Mean Calculator
To estimate an average within 2 units when the standard deviation is about 10, at 95 % confidence, you need 97 observations.
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Standard Error of Difference of Proportions Calculator
Shares of 0.42 among 250 people and 0.35 among 300 differ by 0.07, and this calculator tells you how much that gap would typically vary from sample to sample.
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F Test for Two Variances Calculator
Enter two groups, such as two sets of six readings, and get the F statistic, the first variance divided by the second, with a two-sided p-value.
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Levene Test Calculator
Check whether 2 to 40 groups share the same spread: Levene's test turns each value into its distance from its group mean, compares those distances and returns…
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