Continuous Probability Distributions Calculators
This page presents tools that summarise continuous variables using probability models, providing numerical outputs for ranges of values rather than single fixed outcomes.
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Beta Distribution Calculator
A distribution defined on a fixed interval describes how likely different proportions are when shaped by two tuning values.
Example use: Estimating the chance that a kettle finishes boiling within a certain portion of a minute.
Inputs: alpha, beta, probability type, chosen value, upper bound, output type
Outputs: probability for a chosen range
Visual: a smooth curve showing the density, a rising curve showing cumulative probability, and a table of calculated values
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Cauchy Distribution Calculator
The Cauchy distribution uses a central location and a scale value to describe outcomes that cluster around a centre but allow for very large deviations.
Example use: Modelling the angle of a particle after a scattering event, where extreme deviations are possible.
Inputs: location, scale, probability type, chosen value, upper bound, output type
Outputs: probability for a chosen range
Visual: a density curve with a pronounced centre, a cumulative curve, and a table of supporting values
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Chi-Square Distribution Calculator
A distribution shaped by degrees of freedom describes how sums of squared differences behave across repeated samples.
Example use: Checking whether the variation in the time it takes a kettle to boil each morning is larger than expected.
Inputs: degrees of freedom, probability type, chosen value, upper bound, output type
Outputs: probability for a chosen range
Visual: a right-skewed density curve, a cumulative curve, and a table of values for reference
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Continuous Uniform Distribution Calculator
A distribution with equal likelihood across a fixed interval assigns the same chance to every value between its minimum and maximum.
Example use: Considering how long toast might take to brown when the toaster varies slightly each time.
Inputs: minimum, maximum, probability type, chosen value, upper bound, output type
Outputs: probability density, probability for a chosen range, mean, variance
Visual: a flat density line across the interval and a steadily rising cumulative curve
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Exponential Distribution Calculator
A distribution with a single rate value describes the waiting time between independent events.
Example use: Estimating how long a tap might drip before the next drop falls.
Inputs: rate, probability type, chosen value, upper bound, output type
Outputs: probability for a chosen range, mean, standard deviation, variance
Visual: a decreasing density curve, a rising cumulative curve, and a table of values
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F Distribution Calculator
A distribution defined by two sets of degrees of freedom describes the ratio of two scaled variances.
Example use: Considering how the heights of small plants in a pot might differ when comparing two groups.
Inputs: numerator degrees of freedom, denominator degrees of freedom, probability type, chosen value, upper bound, output type
Outputs: probability for a chosen range
Visual: a right-skewed density curve, a cumulative curve, and a table of values
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Frechet Distribution Calculator
A distribution with a location and scale value models extreme outcomes that occur above a lower bound.
Example use: Estimating the maximum wind speed recorded during a severe storm.
Inputs: location, scale, probability type, chosen value, upper bound, output type
Outputs: probability for a chosen range
Visual: a density curve with a long upper tail, a cumulative curve, and a table of values
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Gamma Distribution Calculator
A distribution shaped by two parameters describes the total waiting time for several independent events.
Example use: Considering how long a phone alarm might ring before someone switches it off.
Inputs: shape, scale, probability type, chosen value, upper bound, output type
Outputs: probability for a chosen range, mean, variance, standard deviation
Visual: a right-skewed density curve, a cumulative curve, and a table of values
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Gumbel Distribution Calculator
A distribution with a location and scale value describes the behaviour of extreme high or low outcomes.
Example use: Estimating the width of pebbles collected during a short walk.
Inputs: location, scale, probability type, chosen value, upper bound, output type
Outputs: probability for a chosen range, mean, standard deviation
Visual: a skewed density curve, a cumulative curve, and a table of values
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Laplace Distribution Calculator
A distribution with a central location and a scale value forms a sharp peak at the centre with heavier tails on both sides.
Example use: Modelling the difference between predicted and actual travel times, where most trips are close to the estimate but some run much longer or shorter.
Inputs: location, scale, probability type, chosen value, upper bound, output type
Outputs: probability for a chosen range
Visual: a pointed density curve, a cumulative curve, and a table of values
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Log-Normal Distribution Calculator
A distribution defined by a mean and spread on a logarithmic scale describes positive values that grow multiplicatively.
Example use: Estimating how long a torch battery might last before dimming.
Inputs: mean on log scale, standard deviation on log scale, probability type, chosen value, upper bound, output type
Outputs: probability for a chosen range
Visual: a right-skewed density curve, a cumulative curve, and a table of values
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Logistic Distribution Calculator
A distribution with a central location and a scale value forms an S-shaped cumulative curve with balanced tails.
Example use: Considering the distance of small throws into a basket during a casual game.
Inputs: location, scale, probability type, chosen value, upper bound, output type
Outputs: probability for a chosen range
Visual: a symmetric density curve, an S-shaped cumulative curve, and a table of values
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Normal Distribution Calculator
A bell-shaped distribution defined by a mean and spread describes values that cluster around the centre with decreasing likelihood further away.
Example use: Estimating how tall a randomly chosen adult might be, based on the average height and typical variation.
Inputs: mean, standard deviation, probability type, chosen value, upper bound, output type
Outputs: probability for a chosen range
Visual: a smooth symmetric density curve, a cumulative curve, and a table of values
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Pareto Distribution Calculator
A distribution with a minimum value and a shape parameter describes outcomes where smaller values are common and larger values become increasingly rare.
Example use: Considering how long a microwave reheats leftovers before reaching a warm temperature.
Inputs: minimum value, shape, probability type, chosen value, upper bound, output type
Outputs: probability for a chosen range
Visual: a decreasing density curve, a cumulative curve, and a table of values
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Rayleigh Distribution Calculator
A distribution with a single scale value describes positive measurements that rise from zero to a peak before tapering off.
Example use: Measuring the size of puddles that form after light rain.
Inputs: scale parameter, probability type, chosen value, upper bound, output type
Outputs: probability for a chosen range, mean, variance, mode
Visual: a rising-then-falling density curve, a cumulative curve, and a table of values
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Student's t-Distribution Calculator
A distribution shaped by degrees of freedom describes how sample means vary when the sample size is limited.
Example use: Estimating the average time it takes to boil a kettle based on a small set of timed measurements.
Inputs: degrees of freedom, probability type, chosen value, upper bound, output type
Outputs: probability for a chosen range
Visual: a bell-shaped density curve with heavier tails, a cumulative curve, and a table of values
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Triangular Distribution Calculator
A distribution defined by a minimum, maximum, and most likely value forms a triangular shape with a clear peak at the mode.
Example use: Timing how long a lift takes to reach a floor during a quiet period.
Inputs: minimum, maximum, mode, probability type, chosen value, upper bound, output type
Outputs: probability for a chosen range, mean, variance, standard deviation
Visual: a triangular density shape, a cumulative curve, and a table of values
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Weibull Distribution Calculator
A distribution shaped by two parameters describes how positive values behave when the likelihood changes steadily across the range.
Example use: Measuring the height of stacked blocks before they fall.
Inputs: shape parameter, scale parameter, probability type, chosen value, upper bound
Outputs: probability for a chosen range, mean, variance, standard deviation
Visual: a smooth density curve showing how likelihood varies across the positive range
Continuous Distributions FAQs
A continuous probability distribution represents values across an uninterrupted range, assigning likelihood to intervals rather than individual points.
These distributions summarise measurements that vary smoothly, supporting comparisons, pattern assessment and probability estimates for numerical ranges.
Skewed data often aligns with Gamma, Log-Normal or Weibull models, while Pareto distributions describe extremely large upper-range values.
Discrete distributions describe countable outcomes, whereas continuous distributions represent values that fill entire intervals without gaps.
The total area under any continuous probability curve equals 1, representing the full likelihood across all possible values.