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🔬 ScienceFree
Bright Newton's ring radius
Locate a bright Newton's ring from its order, the wavelength and the lens curvature, such as order 3 with 589 nm light on a 1 m lens.
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🔬 ScienceFree
Thin film constructive interference calculator
For 550 nm light on a film of index 1.38 with one phase reversal, the thinnest film that reinforces the reflection is 99.6376811594203 nm thick.
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🔬 ScienceFree
Bragg law interplanar spacing calculator
Turns a diffraction peak into a lattice spacing: a Bragg angle of 20° with 1.5406 Å X-rays in first order gives planes 2.25220652945 Å apart.
B
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🔬 ScienceFree
Coherence time calculator
Turns coherence length into time: light with a 3 m coherence length stays coherent for about 10 nanoseconds, the time it takes to cross that distance in vacuum.
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🔬 ScienceFree
Luminous Intensity from Illuminance Calculator
Work out a lamp's candela from a simple lux reading: 125 lux measured 2 metres from a small source means 500 candela in that direction, as long as the meter…
K
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🔬 ScienceFree
Stefan-Boltzmann radiant exitance calculator
A blackbody at 300 K emits 459.300328 W/m², and doubling the absolute temperature multiplies that by 16.
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🔬 ScienceFree
Work Function from Threshold Wavelength Calculator
Enter a photoelectric cutoff of 500 nm and get the minimum energy an electron needs to leave the metal, in electronvolts and joules, plus the matching threshold…
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🔬 ScienceFree
Fiber length from loss budget calculator
Find how far a fiber run can reach on its loss allowance: 7.5 dB spread over fiber losing 0.35 dB/km gives a theoretical maximum of 21.428571 km.
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🔬 ScienceFree
Graded-index fiber mode count calculator
Get a quick mode budget for a graded-index fiber: a V-number of 20 supports about 100 guided modes, polarization included, using the large-V rule of V squared…
B
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🔬 ScienceFree
Reciprocity shutter speed calculator for aperture stop changes
Close the aperture two stops at 1/125 s (0.008 s) and the shutter must stay open four times longer, 0.032 s.
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🔬 ScienceFree
Sunny 16 rule shutter speed calculator for any film ISO
In bright sun at f/16, ISO 100 points to 1/100 s, and the nearest standard shutter setting is 1/125 s.
B
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🔬 ScienceFree
Radiant intensity calculator
A source sending 12 W evenly through 3 sr has an average radiant intensity of 4 W/sr. Enter the power and the solid angle, choose how many decimals you want…
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➗ MathFree
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…
K
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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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…
B
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➗ MathFree
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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➗ MathFree
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…
K
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➗ MathFree
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.
B
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➗ MathFree
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…
B
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➗ MathFree
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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➗ MathFree
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…
B
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➗ MathFree
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.
K
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➗ MathFree
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.
B
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➗ MathFree
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…
K
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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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…
B
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➗ MathFree
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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➗ MathFree
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…
K
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➗ MathFree
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.
K
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➗ MathFree
Chi-Square Critical Value Calculator
With 10 degrees of freedom and a 0.05 significance level, the upper-tail critical value is 18.3070380532751.
K
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➗ MathFree
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…
B
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➗ MathFree
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…
K
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➗ MathFree
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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➗ MathFree
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.
B
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➗ MathFree
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.
B
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➗ MathFree
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…
K
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➗ MathFree
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.
B
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➗ MathFree
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.
K
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➗ MathFree
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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➗ MathFree
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.
K
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➗ MathFree
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…
K
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➗ MathFree
Wilcoxon signed-rank test calculator
Test paired measurements, such as before-and-after readings, without assuming normal differences: for 6 pairs whose positive ranks sum to 19 and negative ranks…
B
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➗ MathFree
Two-Proportion Z-Test Calculator
Compare two success rates from independent groups: 56 out of 100 against 42 out of 100 gives proportions of 0.56 and 0.42 and a pooled rate of 0.49, plus the z…
B
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➗ MathFree
Eta squared calculator
A between-group sum of squares of 24 out of a total of 80 gives an eta squared of 0.3: the grouping factor accounts for 30 % of the observed variance.
B
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➗ MathFree
Odds Ratio Calculator for a 2x2 Table
If 30 people in group 1 have the outcome and 70 do not, against 20 and 80 in group 2, the odds ratio is 2400 over 1400, so the odds are higher in group 1.
K
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➗ MathFree
Weighted moving average calculator
Smooth an ordered series with a sliding weight pattern: with weights 1, 2 and 1, each window covers 3 values, the middle one counts double and the sum is…
B
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➗ MathFree
Atkinson Index Calculator for Income Inequality
An Atkinson index of 0.20 means an equal split at 80 percent of today's mean income would give the same welfare.
B
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➗ MathFree
Double Exponential Smoothing Calculator
When a series opens with 10 and 12, Holt's method starts from a level of 10 and a trend of 2 per period, updates both with every new value and projects as many…
K
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➗ MathFree
Kullback-Leibler Divergence Calculator for Probability Distributions
Measure how far a probability distribution P strays from a reference Q, in nats: identical distributions give 0, and swapping P and Q usually changes the…
K
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➗ MathFree
Two-argument arctangent calculator in degrees
A vector with x of −1 and y of 1 points at 135°, up and to the left. Enter both coordinates, y first and then x, and get the angle in degrees between −180 and…
B
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➗ MathFree
Cotangent of an angle in radians calculator
Enter 0.7853981633974483 radians, a quarter of pi, and the cotangent comes back as 1, with sine and cosine of 0.707106781187 each.
K
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➗ MathFree
Right triangle from hypotenuse and angle calculator
Finish a right triangle from just two values: a hypotenuse of 10 with a 30° angle gives an opposite leg of 5 and another acute angle of 60°, plus the adjacent…
K
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➗ MathFree
Sine of an angle in radians calculator
Get the sine of an angle given in radians: π/2 returns exactly 1, a quarter turn to the top of the unit circle.
B
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➗ MathFree
Ladder angle against wall calculator
Know how steep your ladder stands before you climb: a 5 m ladder with its foot 3 m from the wall leans at about 53.13° to the ground.
K
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➗ MathFree
Shadow length from sun angle calculator
Know how far a shadow reaches before you plan shade or a photo: a pole 2 metres tall with the Sun 45° above the horizon casts a shadow 2 metres long.
B
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➗ MathFree
SSA number of triangles calculator
Know how many triangles your SSA data allow before you solve: sides of 10 and 16 with a 30° angle give an altitude of 8, so two different triangles fit.
B
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➗ MathFree
Cosine of a difference calculator
Find cos(A − B) from two angles: for A of 60° and B of 30° the result is 0.866025403784, the sum of two products of 0.433012701892 each.
K
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