Channels = n(n − 1) / 2
The communication channels formula for the PMP exam, with a free calculator. Enter the team size to get the channel count and what one more person adds, then read the worked example and how the exam tests it below.
What happens when you add one person?
Updated September 2026.
Channels = n(n − 1) / 2
The formula counts the one-to-one communication paths on a project. Every pair of people who talk to each other is one channel. With n people, each person can talk to n − 1 others, which gives n(n − 1) pairs, and dividing by 2 removes the double count, because the path from Ana to Ben is the same path as Ben to Ana. So n is everyone who communicates, including the project manager. A team of 8 plus the PM is n = 9, not 8. That one word in the stem is where most of the wrong answers come from.
PMBOK 8 doesn't print n(n − 1) / 2. What it does say: the number of potential communication channels or paths, one-to-one, one-to-many, and many-to-many, is one of the inputs to communication requirements analysis, the technique used to work out what information each stakeholder needs. That technique is a tool of Plan Communications Management, in the Stakeholders performance domain, next to communication technology, models, and methods. The guide also notes that a complex project with many stakeholders needs a more sophisticated communications management plan than a small one, where the channels are more limited in number. So the formula is a PMP-prep tool for the one-to-one count, and the guide's point is the reason it matters: more people means more paths to plan for.
A project has 8 team members plus you, the project manager. Two more people join. How many new communication channels does the change create?
Type 9 into the calculator above: it returns 36, tells you the next person adds 9, and the comparison grid shows 55 at 11 people. Two people added, 19 channels added. That's the shape of the question the exam asks.
Adding one person to a team of n adds exactly n new channels, one to each person already there. That's why the count climbs so fast: 9 to 10 adds 9, 10 to 11 adds 10, 20 to 21 adds 20. Removing a person from a team of n removes n − 1. The growth is quadratic, not exponential; doubling the team roughly quadruples the channels (10 people is 45, 20 people is 190). Use the rule as a check on your arithmetic: if a question moves a team from 12 to 14, the increase has to be 12 + 13 = 25, and 91 − 66 = 25 confirms it.
PMI doesn't publish a formula list, so no one can promise you a channels question or a count. What's documented: the 2026 Exam Content Outline's People domain, 33 percent of the exam, includes plan and manage communication (defining a communication strategy, establishing a feedback loop, understanding reporting requirements) and engage stakeholders, which includes analyzing and tailoring communication to stakeholder needs. PMBOK 8 puts the channel count inside communication requirements analysis, as above. Expect the formula inside a scenario about a growing team or a new stakeholder group, with the arithmetic as the last step, not the whole question.
| Team Size (n) | Channels | New channels vs. n−1 |
|---|
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The communication channels formula is n(n - 1) / 2, where n is the number of people who communicate on the project, including the project manager. It counts the one-to-one paths between every pair of people. Five people have 5 x 4 / 2 = 10 channels, ten people have 45, and twenty have 190.
Yes. n is everyone who communicates, and the project manager is one of them. A team of 8 plus the project manager means n = 9, so 9 x 8 / 2 = 36 channels, not 28. Read the stem for words like "plus you" or "including the PM" before you pick n.
Adding one person to a team of n adds n new channels, one to each person already there. Going from 9 people to 10 adds 9 channels (36 to 45), and 10 to 11 adds 10 more (45 to 55). Exam questions usually give a starting team, add or remove people, and ask for the change, so calculate both totals and subtract.
PMI does not publish a formula list, so nobody can promise a question. What's documented: PMBOK 8 does not print the formula but lists the number of potential communication channels as an input to communication requirements analysis, a tool of Plan Communications Management, and the 2026 Exam Content Outline's People domain, 33 percent of the exam, includes planning and managing communication and tailoring communication to stakeholder needs. Know the formula and the adding-people rule and you're covered either way.
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