Coin Flip and Dice Rolls

Tools and Utilities • Randomizers and Grouping

Written by STEM Calculators Team Published November 29, 2025 Updated February 24, 2026

Coin Flip & Dice Roll Simulator

Simulate repeated coin flips or dice rolls and see the counts and relative frequencies. The coin includes a simple flip animation to visualize the last outcome.

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How this calculator works

This tool lets you simulate many coin flips or dice rolls and then shows the counts and relative frequencies for each outcome. It is meant to give an intuitive feeling for how experimental results compare with the “ideal” probabilities.

Inputs you control

Simulation type – choose between:
- Coin flips – outcomes are Heads (H) and Tails (T).
- Dice rolls – outcomes are the faces 1 to 6 of a fair die.
Number of trials – how many flips or rolls to simulate (for example 10, 50, or 200). Larger numbers produce smoother frequency estimates but take longer and are harder to read in detail.
Show animation – when checked, the last flip or roll is shown with a short animation:
- for the coin: a small spin before it lands on Heads or Tails;
- for the die: a quick “shake” before showing the final face.
The animation is just a visual aid; the actual random result is determined by the simulation, not by the animation itself.

What happens when you click “Calculate”

The calculator checks that the number of trials is a positive whole number and not too large (to keep the simulation responsive).
It runs the chosen experiment:
- for a coin, it generates Heads or Tails for each trial;
- for a die, it generates one of the faces 1–6 for each trial.
Internally, it uses a random number generator to pick each outcome.
It counts how many times each outcome appears and divides by the total number of trials to get the relative frequency (count ÷ total).
It shows:
- a short summary (how many trials, what the last outcome was);
- a table with counts and relative frequencies for each possible result;
- a quick comparison with the “ideal” probabilities (½ and ½ for the coin, 1⁄6 for each face of the die).
If animation is enabled, the last flip or roll is visualized: the coin spins once and then shows H or T, or the die “rolls” and then shows one of the faces.

You can run the simulation multiple times with the same settings to see how the results vary from trial to trial, or increase the number of trials to watch how the relative frequencies move closer to the expected values. Use Reset to clear the form, and Fill example to quickly set up a sample experiment.

Frequently Asked Questions

What is relative frequency in coin flips or dice rolls?

Relative frequency is the proportion of trials that produced a specific outcome. It is computed as count / total trials for each outcome.

Why do simulated coin flip results not always equal 1/2 and 1/2?

Random experiments vary from run to run, especially with small numbers of trials. As the number of trials increases, the relative frequencies typically move closer to the expected probabilities.

What are the ideal probabilities for a fair coin and a fair 6-sided die?

For a fair coin, Heads and Tails each have probability 1/2. For a fair 6-sided die, each face 1 through 6 has probability 1/6.

Does the animation affect the random result in the simulator?

No. The animation is only a visual display of the last outcome; the outcomes are determined by the simulation's random number generation.

Coin Flip & Dice Roll Simulator

Calculation steps

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Frequently Asked Questions