# PERT Calculator

Created by Maria Kluziak
Reviewed by Dominik Czernia, PhD and Jack Bowater
Last updated: Nov 20, 2022

If you want to predict your project completion times with a high degree of accuracy, you might be interested in this PERT calculator. Use it for business and personal projects and save time and money thanks to proper planning. (By the way: you can learn more about how time and money are related in our TVM calculator!)

For those of you wondering what PERT is, the acronym stands for Program Evaluation and Review Technique - a method of calculating the time it would take to complete a project unmatched in its precision. If you value efficiency and thorough planning, you're in the right place!

Read on to find out more about the usage of PERT, see interesting facts about the method's history, and learn the PERT formula so that you can calculate it even if you don't have this tool handy.

## What is PERT?

PERT (short for Program Evaluation and Review Technique) is an estimation technique used to predict the completion times of various projects with the highest degree of accuracy. Nowadays, it has an abundance of uses, varying from personal projects to big business enterprises. Its origins, however, might come as a surprise. PERT was developed and first applied by the United States Department of Defence on their Ballistic Missile development program. The sheer size of the enterprise made it susceptible to delays, and time was critical, so PERT was developed to maximize its efficiency.

The PERT formula includes three things:

• The optimistic time estimate ($\small O$) - the ideal situation where everything goes right. Unfortunately, that's rarely the case.
• The pessimistic time estimate ($\small P$) - where everything goes wrong.
• The most probable time estimate ($\small M$) - the most likely situation with some delays and problems, but nothing too drastic.

The time estimates are combined in the following way:

$\scriptsize \text{PERT time estimate} =\frac{O+4\times M + P}{6}$

While calculating PERT, it's a good idea to account for the standard deviation, which we usually denote as $\small \text{SD}$. Knowing the $\small \text{SD}$ is useful, as it can give you an idea of just how accurate the calculation is. In practice, this means even better planning - for example, you can give your customer a range in which they can expect the project to be finished. Calculating the standard deviation for the PERT formula goes as follows:

$\scriptsize \text{SD} = \frac{P-O}{6}$

🙋 Expand your knowledge about the standard deviation parameter by checking out our normal distribution calculator.

## How does this PERT calculator work?

1. Decide if you want the PERT calculator to show you the standard deviation as well as the time estimate.
2. Input the following variables:
• Your most probable time estimate; and
• Optionally, your desired completion time.
3. At the bottom of the calculator, you will see your PERT time estimate, the standard deviation, and the probability that you will complete your project in the desired time (if you provided the desired completion time).
4. Additionally, in the Advanced mode, you can check the calculated z-score, which we used to estimate the mentioned probability.

🔎 If you want to learn more about z-scores, we have our Z-score calculator waiting for you. 🙂

## Example of using the PERT formula

You now know what PERT is and how to calculate it. Still, let's go through an example to clear any remaining doubts.

Let's imagine you decided to build a new fence around your property and want to accurately assess how much time you'll need to do it. Based on your daily availability, if the weather conditions are good, you should be able to finish the projects in five days. Unfortunately, the weather forecast predicts there might be some scattered storms in the next few days, and it looks like the worst-case scenario is a total of nine days of work. Seven days seem the most reasonable, accounting for some delays due to the weather, but not being overly pessimistic. So, all in all, you have:

• An optimistic estimate $\small O = 5\ \text{days}$;
• A pessimistic estimate $\small P = 9\ \text{days}$; and
• A most likely estimate $\small M = 7\ \text{days}$.

Let's put these numbers into the PERT formula:

\scriptsize \begin{align*} \text{PERT time estimate} &=\frac{O+4\times M + P}{6}\\[1.0em] &=\frac{5+4\times 7 + 9}{6}\\[1.0em] &=\frac{5+28 + 9}{6}\\[1.0em] &=\frac{42}{6}\\[1.0em] &=7 \end{align*}

The standard deviation is:

\scriptsize \begin{align*} \text{SD} &= \frac{P-O}{6}\\[1.0em] &= \frac{9-5}{6}\\[1.0em] &= \frac{4}{6}\\[1.0em] &= 0.67 \end{align*}

According to the program evaluation and review technique estimate, you should be able to finish your fence in 7 days, with a standard deviation of 0.67 days (which means about 16 hours).

✅ If you're wondering how we came up with 16 hours, given its value in days, you should definitely visit our time unit converter to learn how to convert between different time units.

Maria Kluziak
Optimistic
hrs
Pessimistic
hrs
Most probable
hrs
Desired completion time
hrs
Time estimate according to program evaluation and review technique:
PERT estimate
hrs
Standard deviation (SD)
hrs
Probability of completion
%
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