A clear method behind every flip

How randomness works

The single flipper uses Web Crypto to obtain an unsigned 32-bit value. Even values become heads and odd values become tails. The batch simulator uses random bytes: values below 128 become heads, and the other half become tails. Both mappings divide the possible values evenly.

The result is chosen before the animation. The browser supplies cryptographically strong pseudorandom values; this site does not claim to use a physical coin or a quantum source. See MDN’s Web Crypto documentation.

How probabilities are calculated

The calculator assumes independent fair flips. Exact heads counts use the binomial formula. Cumulative results sum the appropriate counts; upper tails use symmetry to avoid subtracting a nearly-one value. Streak results track unfinished runs and count each sequence’s first successful run, avoiding duplicate counting of overlaps.

Calculations use floating-point arithmetic and rounded display values. Small percentages use scientific notation. The calculator explains the events and assumptions next to the results.

What stays in your browser

Flip results, custom labels, and simulation data stay in the current page’s memory. Reloading clears them. Downloading a CSV or copying a result is an explicit action you control. Calculator links contain numeric settings in the URL fragment; custom labels are not put in URLs.

These statements describe the tools’ handling of inputs, not all website infrastructure: hosting providers receive normal page requests, and fonts may be requested from Google Fonts.

How guides are maintained

Guides distinguish ideal mathematical examples from physical tossing and historical accounts. Source links appear on each guide. Review dates record content review, rather than changing automatically with every deployment. Calculated examples are checked against small, enumerable outcome sets.

The current revision was prepared with AI assistance and checked against the linked sources and implementation. It does not claim independent laboratory testing or professional certification.

Contact and corrections

For support or to report a mistake, email [email protected]. Include the page URL, input values, and what you expected to happen. Please avoid sending sensitive personal information.

Explore the tools

Try the coin flip simulator to download a batch, or browse the guides for worked examples.