Dice look simple, but the moment you roll more than one the odds stop being obvious, and this calculator works them out exactly for you. Choose how many dice you are rolling, how many sides each die has, and the total you care about, and it returns the probability of hitting that total as a clean percentage and as easy-to-read odds such as 6 in 36. You can ask for the chance of rolling exactly your target, at least your target, or at most your target, which covers almost every question that comes up in board games, tabletop role-playing, teaching and homework. The answer is not an estimate or a simulation. The calculator builds the full distribution of every possible sum by starting with one die and combining it with each extra die in turn, a method that counts every equally likely outcome precisely, so the figures are exact even for large handfuls of dice. The total number of outcomes is simply the number of sides raised to the power of the number of dice, and the probability of any result is the count of matching outcomes divided by that total. Seeing the answer this way makes the shape of dice odds clear: middle totals are far more likely than the extremes, because there are many more ways to reach them. That is why a total of 7 turns up so often with two ordinary dice while 2 and 12 are rare. Sensible limits keep the calculation fast and the numbers meaningful. Set your dice, sides, target and condition below, and the probability updates instantly as you type.
The probability of a dice sum is the number of outcomes that match your condition divided by the total number of possible outcomes. For N dice each with S sides, the total number of outcomes is S raised to the power N. The count of ways to reach each sum is found by combining the distributions of the dice one at a time, then the calculator adds up the counts for exactly, at least or at most your target.
probability = matching outcomes / total outcomes
total outcomes = SN
Roll two ordinary six-sided dice and ask for a total of exactly 7. There are 6 × 6 = 36 equally likely outcomes. Six of them add to 7, namely 1+6, 2+5, 3+4, 4+3, 5+2 and 6+1. The probability is 6 / 36 = 0.1667, or 16.67 percent, which you can read as 6 in 36, or 1 in 6.
This calculator is for board gamers, tabletop role-players, teachers, students and anyone curious about the odds of a dice roll, whether for a game decision or a probability exercise.
There are 36 equally likely outcomes and 6 add to 7, so the chance is 6 in 36, which is 1 in 6, or about 16.67 percent. Seven is the most likely total with two dice.
Count the outcomes that produce the target and divide by the total outcomes, which is the number of sides raised to the power of the number of dice.
Exactly means the sum equals your target, at least means your target or higher, and at most means your target or lower. The calculator adds the matching outcomes for the condition you pick.
There is only one way to roll 2 and one way to roll 12, but six combinations add to 7. More combinations means a higher probability, so the middle sums are the most common.
If you've found a bug, or would like to contact us, or learn more about James Graham and Calculate.co.nz.
Calculate.co.nz is partnered with Interest.co.nz for New Zealand's highest quality calculators and financial analysis.
All calculators and tools are provided for educational and indicative purposes only and do not constitute financial advice.
Calculate.co.nz is proudly part of the Realtor.co.nz group, New Zealand's leading property transaction literacy platform, helping Kiwis understand the home buying and selling process from start to finish. Whether you're a first home buyer navigating your first property purchase, an investor evaluating your next acquisition, or a homeowner planning to sell, Realtor.co.nz provides clear, independent, and trustworthy guidance on every step of the New Zealand property transaction journey.
Calculate.co.nz is also partnered with Health Based Building and Premium Homes to promote informed choices that lead to better long-term outcomes for Kiwi households.
Calculate.co.nz is hosted in Auckland via SiteHost new Zealand.
All content on this website, including calculators, tools, source code, and design, is protected under the Copyright Act 1994 (New Zealand). No part of this site may be reproduced, copied, distributed, stored, or used in any form without prior written permission from the owner.
About & trust: Why Calculate is NZ's most comprehensive · By the Numbers · How we compare · Editorial standards · How we keep data current · NZ finance glossary · Research & data · Financial literacy NZ · About · Privacy policy · Terms of use
Reviewed and maintained. Last reviewed 2026-06-07 and checked on a twice-monthly cycle against IRD, RBNZ and Stats NZ. How we keep data current.
© 2026 Calculate.co.nz. All rights reserved. Building free NZ calculators since 2011.