Back-of-the-envelope numbers, said naturally
Estimate out loud, round freely, and say what the numbers mean for your design.
What they’re listening for
- • Can you estimate scale without a calculator?
- • Do you round sensibly?
- • Do the numbers change your design?
Nobody expects exact math. The trick is to round to easy numbers, say the rounding out loud, and then say what the number means. A day has 86,400 seconds, but most engineers just call it “about a hundred thousand” to keep the math easy.
Stiff vs. natural
Interviewer: “Let's say we get about 100 million redirects a day. What does that look like?”
Sounds stiff
“100 million divided by 86,400 is… (long pause) …1,157.4 requests per second.”
Sounds natural
“Okay, quick math. A day is roughly a hundred thousand seconds, so 100 million a day is a bit over a thousand requests a second. Traffic isn't flat, though, so at peak, call it three to five thousand. That's a lot for one database, but redirects are really cacheable, since popular links get clicked over and over. So I'd put a cache in front and expect most reads to never touch the database.”
- “Roughly a hundred thousand seconds” makes the math easy to do out loud.
- “A bit over a thousand” is precise enough.
- Thinking about peak traffic shows real-world experience.
- The number leads to a decision (add a cache). That's the point of estimating.
Interviewer: “And how much storage do we need?”
Sounds stiff
“Each record is 500 bytes. 100 million records per month multiplied by 500 bytes is 50,000,000,000 bytes per month.”
Sounds natural
“Let's say each link is about 500 bytes, so the long URL plus a bit of metadata. A hundred million new links a month times 500 bytes is about 50 gigs a month, so call it 600 gigs a year. Over five years we're at roughly three terabytes. That's honestly not scary. It fits on one big database, so storage isn't our problem. Read traffic is.”
- “Gigs” and “call it” are how engineers say numbers casually.
- Going from a month to a year to five years makes the size easy to judge.
- “Storage isn't our problem, reads are” tells the interviewer where to focus.
Saying numbers casually
- “Okay, quick math…”Starting an estimate.
- “Call it…”Rounding to an easy number.
- “Roughly… / Ballpark…”Saying it's an estimate.
- “A bit over / a bit under…”Close enough is fine.
- “At peak, maybe three or four times that.”Thinking about traffic spikes.
- “So what that tells me is…”Turning a number into a decision.
Humor and life talk
Works well
- • A light comment about rounding (“I'm going to round pretty aggressively here”)
- • Catching your own mistake with a smile (“Wait, that's way too many zeros”)
Skip it
- • Saying “I'm bad at math.” It undercuts you, even as a joke.
- • Joking instead of doing the estimate
Example: “Wait, that's way too many zeros. Let me redo that. Okay, fifty gigs, not fifty terabytes.”
Now say it out loud
Rehearse with the AI interviewer and get feedback on your answers.