Google Sheets BETADIST Function: Syntax, Examples & Tips

What Is BETADIST?

BETADIST evaluates the cumulative beta distribution, a family of probability distributions defined on a bounded interval (by default from 0 to 1). Because it lives between two limits, the beta distribution is a natural model for proportions and rates: conversion rates, completion percentages, the share of time a task takes up, or an uncertain probability.

Two shape parameters, alpha and beta, control its form. Equal values give a symmetric curve centred on the middle of the interval. A larger alpha pushes the bulk of the curve towards the upper bound; a larger beta pushes it towards the lower bound. When both are 1, the distribution is flat (uniform).

BETADIST is a legacy function kept for compatibility with older spreadsheets. Its modern equivalent is BETA.DIST. =BETADIST(x, a, b) gives the same answer as =BETA.DIST(x, a, b, TRUE). BETA.DIST also lets you return the density instead of the cumulative probability by setting cumulative to FALSE, so prefer it in new work.

How BETADIST Works

BETADIST always returns a cumulative probability: the chance that a beta-distributed variable is less than or equal to value. The answer is a number between 0 and 1. It cannot return the density (the height of the curve); for that, use BETA.DIST(value, alpha, beta, FALSE). Densities are not probabilities and can be greater than 1.

If your quantity runs on a scale other than 0 to 1, supply lower_bound and upper_bound. Google Sheets rescales value into that interval before calculating.

Basic Examples

Cumulative probability

=BETADIST(0.5, 2, 3)

Returns 0.6875: with alpha 2 and beta 3, there is a 68.75% chance the variable is at or below 0.5.

Density at a point (modern function)

=BETA.DIST(0.5, 2, 3, FALSE)

Returns 1.5, the height of the curve at 0.5. BETADIST cannot do this.

Custom bounds

=BETADIST(50, 2, 3, 0, 100)

Same shape on a 0–100 scale. Returns 0.6875, because 50 sits halfway along the interval.

Probability between two values

=BETADIST(0.6, 8, 12) - BETADIST(0.3, 8, 12)

The chance that the variable falls between 0.3 and 0.6.

Using BETADIST for Conversion Rates

A common Bayesian shortcut: after observing s successes and f failures, starting from a flat prior, the conversion rate can be modelled as Beta(s + 1, f + 1). With 40 conversions out of 400 visits:

=1 - BETADIST(0.12, 41, 361)

estimates the probability that the true conversion rate is above 12%.

Common Use Cases

• A/B testing: probability that a conversion rate exceeds a target
• Project management: PERT-style estimates of task duration between a minimum and maximum
• Quality: modelling the proportion of defective items
• Risk analysis: uncertain percentages in simulations

Common Errors

• #NUM!: alpha or beta is zero or negative, or value is outside the bounds.
• #NUM! from bounds: lower_bound is not less than upper_bound.
• #VALUE!: An argument is text that cannot be read as a number.
• Passing a cumulative flag: BETADIST has no cumulative argument. A fourth argument is read as lower_bound, which gives unexpected results. If you need that flag, switch to BETA.DIST.

Tips and Best Practices

• To go the other way, from a probability back to a value, use BETAINV.
• The mean of a standard beta distribution is alpha ÷ (alpha + beta). Use this to sanity-check your parameters.
• Plotting the density over a column of values from 0 to 1 is a quick way to see the shape you have chosen.

Related Functions

• BETAINV: inverse of the cumulative beta distribution
• BINOMDIST: probabilities for counts of successes
• AVERAGE: the mean of a data set
• ROUND: tidy up probability results
• IF: turn a probability into a decision