How to Answer Estimation Questions
Estimation interviews typically last from 40 minutes to an hour.
Some interviewers will ask two or three questions with little follow-up. Others may ask a single estimation question and spend 15 minutes diving deeper into the details.
Remember that, similar to other PM interviews, interviewers don’t expect you to arrive at a correct answer. They’re interested in how you solve problems given limited information; a situation you’ll find yourself in frequently as a PM.
The key to solving ambiguous problems is to break them down into manageable pieces that you can address individually. Once you’ve gotten a handle on the component pieces, you can build those components back up in a way that’ll result in a reasonable estimation.
Practice is critical when it comes to estimation questions. You’ll build confidence in your ability to break down problems and estimate unknowns with time. If you’re new to the process, a helpful tip is to learn benchmark facts that could reasonably come up in estimation interviews.
Facts like the current population of the world, average global life expectancy, the cost of the latest Google Pixel, or your target company’s annual revenue prove helpful more often than you might think. Having a few figures like these in your back pocket can help jump-start your process and ground your answer in reality.
Review benchmark facts found in Exponent’s Estimation Fact Sheet to jump-start your estimation interview practice.
A framework for answering estimation questions
After reviewing benchmark facts, we recommend familiarizing yourself with the following 5-step framework for estimation questions.
Step 1: Scope the problem
Step 2: Break the problem down
Step 3: Estimate unknowns
Step 4: Answer
Step 5: Explain why you’re wrong
Let’s work through an example to illustrate. Assume you’ve been asked:
“Estimate the number of stacked quarters needed to reach the height of the Empire State Building”
Step 1: Scope the problem
Ask questions to clarify the scope of the problem. This will prevent you from taking the question in the wrong direction and give you a chance to glean helpful information from your interviewer.
For example, if you were asked to estimate the weight of a school bus, you’d want to ask:
- Does the weight estimate include a full tank of gas?
- Does the weight estimate include humans inside the school bus?
- How many people is the school bus expected to seat in total?
Instead of giving you a straight answer, your interviewer may tell you to make assumptions about the scenario as needed. If this happens, state any assumptions that feel reasonable to you and make the problem easier.
For instance, if your interviewer declines to answer your questions about the school bus's weight, assume the gas tank is empty.
For our sample question “Estimate the number of quarters needed to reach the height of the Empire State Building” you’d want to state a few assumptions up-front.
For example, it’s reasonable to assume that the height of an average building is mainly made up of floors.
With a landmark skyscraper like the Empire State Building, it’s reasonable to assume that there are features like a vaulted ceiling on the ground floor.
You may also have an image of the Empire State Building in your mind, and recall that it has a large antenna on top.
High ceilings and an antenna would add to your height estimate. You can include them up-front, or state to your interviewer that you’ll ignore them for now and come back to them later. The key is to communicate with your interviewer and go with whatever direction they give you.
Let’s assume for now that you’ll ignore features like a vaulted ceiling or an antenna, and estimate height according to the sum of the building’s floors.
Step 2: Break down the problem
Once you’ve scoped the problem, you can break it down into manageable pieces.
First, find a reasonable high-level equation that describes the problem.
Then, based on that equation, break down each factor further until you’re left with something you can reasonably estimate.
As you break down the problem, you’ll likely have to make more simplifying assumptions. That is expected; simply communicate your thought process to your interviewer.
If you believe an edge case (e.g. whether or not there are vaulted ceilings) is critical to your estimation, be sure to state your assumptions up-front. If you decide that it’s not worth identifying that component, communicate this to your interviewer as well.
Our example question “Estimate the number of quarters needed to reach the height of the Empire State Building” breaks down to the following high-level equation:
Number of quarters = Height of the Empire State Building / Height of a quarter
By framing the problem as an equation, it’s clear that you only need to come up with 2 numbers to solve this problem:
- The height of the Empire State Building
- The height of a quarter
Step 3: Estimate unknowns
Once you’ve broken the problem down into estimable pieces and explained your approach, it’s time to estimate numbers.
Break down each component until you arrive at something you feel confident estimating.
Remember, the numbers don’t matter. There are always other ways to slice the problem or to break down a factor into something you can work with.
Here are some tips to get you going if you’re drawing a blank.
- Recall any benchmark facts you memorized. Is there anything helpful?
- Estimate using a proxy value. Can you make reasonable assumptions using a known fact as a jumping-off point?
- Segment diverse groups. Don’t try to make assumptions about the behavior or diverse groups. Instead, segment in a way that’s meaningful to your question, and sum the individual estimates.
- Use a personal reference. Can you relate the unknown quantity to something you do know, even if it’s anecdotal? Don’t forget to communicate that you’re offering anecdotal and possibly biased information to your interviewer.
Learn more tips for estimating unknowns and doing back-of-the-envelope calculations for estimation questions.
As you estimate, don’t forget to gut-check your numbers. If they feel reasonable, go ahead. If something feels off, revisit your math or break the problem down further.
For our example question, recall your high-level equation:
Number of quarters = Height of the Empire State Building / Height of a quarter
You need to come up with estimates for the height of the Empire State Building and the height of a quarter.
Let’s assume you start by estimating the height of the Empire State Building.
Recall that you’ve stated to your interviewer that you’re assuming that the height of the Empire State Building is roughly equivalent to the sum of the height of its many floors. As an equation, this would be:
Empire State Building Height ≈ Number of floors × Average height of a floor
You might state the following reasonable assumptions:
- “The Empire State Building is known to be a very tall building, so it’s safe to assume it has a lot of floors, perhaps on the order of 100.”
- “It’s a commercial building, so its floors are likely to be the standard size for an office building, I estimate that to be around 12 ft.”
This gives you a height estimate of 1200ft for the core building, which feels reasonable.
Next, let’s estimate the height of a quarter.
One approach for estimating the height of a quarter would be to make a reasonable comparison. A quarter is small and hard confidently visualize. Instead, you might visualize a larger relevant object, like a $10 roll of quarters, and break that down.
Your equation would then be:
Height of a single quarter = Height of a roll of quarters / Number of quarters in $10
These variables are easier to estimate. The height of a roll of quarters fits decently well in a hand, so you might estimate the roll of quarters to come to about 4 inches.
A $10 roll of quarters is equal to 40 quarters. If you plug these values into your single quarter equation, you’d get 1/10th of an inch per quarter. This seems fairly reasonable.
You now have the following estimates for your 2 variables:
- Height of the Empire State Building ≈ 1200ft
- Height of a single quarter ≈ 1/10th of an inch
Step 4: Answer
Next, plug in your estimates for key variables into your high-level equation, and compute the total. Be sure to:
- Convert any mismatched units before the final calculation
- Round difficult numbers for simplicity
- Communicate each step of your computation
If you’ve been gut-checking along the way, you should feel reasonably confident in your answer, but we recommend gut-checking your final number as well.
Review tips for making mental math easier in estimation questions.
If something feels very wrong, it’s worth checking the assumptions you’ve made along the way and double-checking your math.
For our example question, recall your high-level equation:
Number of quarters = Height of the Empire State Building / Height of a quarter
Also recall your variable estimates:
- Height of the Empire State Building ≈ 1200ft
- Height of a single quarter ≈ 1/10th of an inch
If you plug the variable estimates into the high-level equation, the number of quarters = 1200 ft / 1/10th inch per quarter.
Rounding down for simplicity, 1/10th of an inch (per quarter) is approximately 1/100th of a foot per quarter. Therefore, 100 quarters per foot x the 1200 ft tall building = 120,000.
You end up with a final estimate of 120,000 quarters in total.
It can be difficult to gut-check a value like this without context, but let’s assume this feels reasonable given that you felt confident in your intermediate gut-checks.
Step 5: Explain why you’re wrong
This last step is crucial.
Your answer is wrong.
Based on your final gut check, you should have a sense of whether you’ve under or over-estimated.
Take 1-2 minutes to share your critiques with your interviewer. Summarize any estimations that felt like guesses. Describe what you’d reconsider if you had more time, taking care to list any elements you ignored for simplicity that, upon review, may have large implications for your answer. If you’re unsure of where you may have made mistakes, it can be helpful to ask yourself what facts you’d have liked to have had on hand when you were first given the question. How did you make do without that information? What substitutions and assumptions were necessary? If you used any of the recommended strategies above (estimation by proxy, personal reference, etc). be sure to list the potential errors in those approaches.
Being proactive here demonstrates important PM skills like critical thinking, and communication. A thorough recap also preempts follow-up questions from your interviewer.
As we close the example question “Estimate the number of quarters needed to reach the height of the Empire State Building” your estimate of 120,000 quarters seems to be fairly reasonable.
Looking at your assumptions, however, there are some obvious areas where you likely miscalculated.
You might say to your interviewer:
”When estimating the height of the Empire State Building, I assumed that because the Empire State Building is known to be a tall skyscraper, it must have around 100 floors. This is the first assumption I would want to check given more time. I also chose to ignore any vaulted ceilings, and, more importantly, the Empire State Building’s antenna. Looking at it from the ground, the antenna doesn’t seem to be that large, but this could be a case of distorted perspective. I also neglected to consider a basement or any below-ground floors.
When estimating the height of a quarter, I assumed a $10 roll of quarters to be about 4 inches in length because it fits comfortably in my hand. This seems suspect, and an incorrect estimate here could have a huge impact on my estimate. All of these factors have a bearing on the accuracy of my answer.”
