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.
Relative standard deviation
A standard deviation of 2.5 on a mean of 50 is an RSD of 5 %. Enter the two summaries you already hold and get the spread as a percentage of the mean, ready for…
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Roulette payout calculator
25 chips on red with 7 as the winning number pay 25 and bring 50 chips back to you. Name the bet, the stake and the pocket that landed on a single-zero wheel…
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Sampling error calculator
A sample mean of 52 against a population mean of 50 is a sampling error of +2, so the sample overestimates.
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Sensitivity and specificity calculator
90 true positives, 10 false negatives, 80 true negatives and 20 false positives give a sensitivity of 90 % and a specificity of 80 %.
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Simpson's diversity index
Counts of 10, 20, 5 and 15 give 50 individuals in four species and a diversity index just above seven in ten: the chance that two random individuals differ.
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Stem-and-leaf plot calculator
Seven scores from 12 to 31 become three rows, and stem 2 holds the leaves 1, 3, 3 and 5 for the values in the twenties.
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Third quartile calculator
Find the third quartile of a list in one step: for the values 1 to 8, Q3 is 6.25, the point with three quarters of the data at or below it.
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Two envelopes paradox calculator
See the arithmetic behind the two envelopes paradox: keeping the opened envelope is worth exactly what you saw, while switching appears worth 1.25 times as much…
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Uniform distribution calculator
Enter the bounds of a continuous uniform distribution and get the essentials: on 0 to 10 the mean is 5, the density is 0.1 and the chance of a value at or below…
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Upper and lower fence calculator
Find the cut-offs that flag outliers in a box plot: for the numbers 1 to 9, Q1 is 2.5, Q3 is 7.5 and the fences fall at −5 and 15, so any value outside them…
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Wilcoxon rank-sum test calculator
Compare two independent groups without assuming a normal distribution: for samples of 5 and 6 values that do not overlap, the rank sum of the first is 45, the…
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Z-test calculator
Check whether a sample mean fits a hypothesized mean when the population standard deviation is known: a mean of 105 against 100, with a standard deviation of 15…
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Bertrand paradox calculator
With both ends picked at random on the circle, a chord is longer than the side of the inscribed equilateral triangle with probability 1/3, while two other…
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Chebyshev's theorem calculator
At least 75 percent of any data set with a finite variance lies within 2 standard deviations of its mean, bell-shaped or not.
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Coin flipper
Ten fair flips with seed 42 always give the same sequence, THTTHTHTTH: 4 heads and 6 tails. Change the number of flips or the seed to run a new experiment and…
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Combinations without repetition
Choosing 3 items from 10 distinct ones, with no repeats and order ignored, gives 120 combinations.
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Confusion matrix calculator
Eight cases compared with their predictions give 3 true positives, 3 true negatives, 1 false positive and 1 false negative.
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Critical value calculator
At a 0.05 significance level the critical z is about 1.96 for a two-tailed test and about 1.645 for a one-tailed one.
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D20 dice roller
Seed 42 always lands on 17: the same seed always gives the same face of a fair twenty-sided die, so a game master, a player or a reviewer can check the roll…
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Decimal random number generator
With bounds 0 and 1 and seed 42 you always get 0.2523451748: the same bounds, seed and number of decimals replay the same draw.
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Dice expected value and variance
One fair six-sided die has an expected value of 3.5 and a variance of 35/12. Enter the sides and the number of rolls to get both figures for the sum: how large…
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Dispersion calculator
For 2, 4, 4, 4, 5, 5, 7 and 9 you get a range of 7, a variance of 4 and a standard deviation of 2, all three at once.
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D&D dice roller
Type 2d6+3 with seed 42 and you get faces 1 and 5 plus the modifier 3, for a total of 9, every time.
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Error propagation calculator
Multiply 2 ± 0.1 by 3 ± 0.2 and you get 6 with a combined standard uncertainty of 0.5, plus the share each input adds.
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False positive rate calculator
5 false alarms among 100 truly negative cases give a false positive rate of 0.05: 5 false positives divided by 5 plus 95 true negatives.
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Fisher's exact test calculator
The 2x2 table 8, 2, 1, 5 gives a two-sided p-value of 5/143, below the usual 0.05 level. Fisher's exact test stays exact with small samples and near-empty…
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Fractional odds converter
Enter a fractional price and see its three other faces: 5/2 becomes decimal odds of 3.5, an implied chance of about 28.57% and 2.5 units of profit for every…
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Histogram calculator
Get the frequency table behind a histogram: the values 1, 2, 2, 3, 5, 7, 8 and 9 split into four bins of width 2 give counts of 3, 1, 1 and 3.
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Hypergeometric distribution
Find the chance of drawing an exact number of marked items without putting any back: from an urn of 10 balls with 4 red, drawing 3 gives exactly one red with…
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IQR calculator
Get the spread of the middle half of your data: for the numbers 1 to 8, Q1 is 2.5, Q3 is 6.5 and the interquartile range is 4.
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Joint probability calculator
Work out the chance that two events both happen: with P(A) of 0.5 and P(B) of 0.4, independent events give 0.2, or 20%.
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Lottery jackpot probability
Work out your exact chance of hitting a lottery prize: in a 6-from-49 game, matching all six numbers is 1 in 13,983,816, and you can ask for lower tiers such as…
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MAD calculator
Find how far your numbers sit from their mean on average: for 2, 4, 4, 4, 5, 5, 7 and 9 the mean is 5, the distances add up to 12 and the mean absolute…
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McNemar's test calculator
For the paired counts 59, 6, 16 and 80, McNemar's test uses only the 22 discordant pairs and gives a p-value just above 0.05, so the change is not significant…
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Median calculator
For 1, 3, 3, 6, 7, 8 and 9 the median is 6, with three values on each side. Paste the numbers in any order: they are sorted for you, and an even count takes the…
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MSE calculator
Four predictions whose squared misses add up to 0.6 give a mean squared error of 0.15. Paste the predicted and actual values in matching order; each gap is…
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Normal approximation calculator
For 100 trials with a 0.5 chance of success, the normal approximation puts the chance of exactly 50 successes at about 8%, using a mean of 50, a standard…
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Or probability calculator
With P(A) of 0.3, P(B) of 0.4 and an overlap of 0.1, the chance that A or B happens is 0.6: add both, then subtract the overlap once so it is not counted twice.
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Order from least to greatest
Enter 5, 1, 4, 2, 3 and get 1, 2, 3, 4, 5: smallest first, largest last. Duplicates stay, and numbers are compared by value, not as text, so 10 never lands…
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Password combination calculator
Twenty-six lowercase letters and 8 characters give 208,827,064,576 possible passwords. Enter how many symbols each position can use and how long the password…
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Permutation with repetition
The letters of BANANA can be rearranged into 60 distinct words: 6 letters, with A three times and N twice.
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Pie chart percentage calculator
The amounts 1, 1 and 2 add up to 4, so they become a quarter, a quarter and half of the pie. Paste your category values and get slice percentages that always…
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Post-test probability calculator
With a pre-test probability of 0.01, a positive result on a test with sensitivity 0.9 and specificity 0.95 raises the chance of disease only to 0.153846153846.
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Probability to fraction converter
A probability of 0.25 becomes the reduced fraction 1/4, and 0.375 becomes 3/8. Enter any probability from 0 to 1 and get the simplified numerator and…
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Quartic regression calculator
Data from x⁴+2x³−x²+3x+5 at x of 0 to 4 returns the coefficients 1, 2, −1, 3 and 5 with an R² of 1.
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Random dice roller
Two six-sided dice with seed 42 land on 1 and 5 for a total of 6, out of a possible 2 to 12. Choose how many identical dice to throw, how many sides each has…
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Relative error calculator
A reading of 105 against a true value of 100 misses by 5, a relative error of 0.05 or 5%. Enter the measured and the true value to get the absolute relative…
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Sampling distribution of a sample proportion
With a true share of 0.6 and samples of 100, the sample proportion centres on 0.6 with a variance of 0.0024 and a standard deviation equal to its square root.
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Skewness calculator
The list 1, 2, 3, 4, 10 has a mean of 4 and a positive skewness, because the 10 stretches the right tail.
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Standard error calculator
A sample standard deviation of 10 with 25 observations gives a standard error of exactly 2, since 10 is divided by the square root of 25.
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Two dice probability
Pick a total from 2 to 12 and see how many of the 36 rolls of two dice produce it: a 7 comes up in 6 ways, so 6/36 or 1/6.
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Weibull distribution calculator
Get the Weibull density or cumulative probability at a point: with shape 2, scale 1 and x of 1 the density is 2/e.
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DPMO calculator
Twenty-five defects in 200 assemblies with 5 inspection points each give 25,000 DPMO: defects scaled to a million chances to fail.
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Associative property of addition
(2 + 3) + 4 and 2 + (3 + 4) both equal 9, so the associative property holds. Enter any three numbers and see both groupings worked out side by side, with a…
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Area of a quadrilateral
The rectangle with corners at (0, 0), (4, 0), (4, 3) and (0, 3) has an area of 12. Enter the four corners of any quadrilateral as coordinates, in order around…
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Average percentage calculator
Scores of 80, 90 and 70 percent average out to 80 percent. Paste exam scores, conversion rates or survey results already written as percents, with or without…
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Average calculator
The average of 2, 4, 6, 8 and 10 is 6: the numbers add up to 30 and there are 5 of them. Paste a list of scores, prices or readings and get the plain…
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Base of a triangle calculator
A triangle with an area of 10 and a height of 4 has a base of 5: double the area and divide by the height.
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Bessel function calculator
J₀(1), the Bessel function of the first kind of order 0 at 1, is about 0.765197686558. Enter a whole-number order from 0 up and a real value, and get Jn(x) for…
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Convert fraction to percentage
Enter a numerator and a denominator and read the percentage: 3/4 is 0.75 as a decimal and 75%, and an improper fraction such as 5/4 gives 125%.
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