back of the envelope

USAGE SUMMARY

The phrase "back of the envelope" is a correct and usable part of a sentence in written English.
It is typically used to mean a rough calculation or estimate that is made without taking the time to do a detailed or sophisticated analysis of the information. For example, "I did a quick back of the envelope calculation to estimate how much the project would cost."

✓ Grammatically correct

News & Media

Academia

Science

Human-verified examples from authoritative sources

Exact Expressions

23 human-written examples

Back of the Envelope Physics. 3 Units.

Stanford University

Science on the Back of the Envelope.

Stanford University

Kind of the back of the envelope calculation that accountants do.

Yale University

This chapter covers "back of the envelope" techniques for estimating the bandwidth of transistor amplifiers.

Intuitive Analog Circuit Design A Problem-Solving Approach using Design Case Studies

"Quite frankly, by the back of the envelope, they need more money," he said.

The Washington Post

Wagner signed the back of the envelope.

Forbes

Human-verified similar examples from authoritative sources

Similar Expressions

37 human-written examples

Ellenberg punctures this argument with a simple back-of-the envelope sketch.

The Guardian - Books

"A back-of-the-envelope calculation..

The New Yorker

Let's try back-of-the-envelope calculations.

The Guardian - Tech

That back-of-the-envelope figure isn't disastrous.

The New York Times

"It's back-of-the-envelope stuff with lots of assumptions".

The New York Times

Expert writing Tips

Best practice

When presenting a "back of the envelope" calculation, briefly outline the assumptions and simplifications you've made.

Common error

Avoid presenting a "back of the envelope" calculation as a definitive answer. Always acknowledge its limitations and potential for error.

Linguistic Context

The phrase "back of the envelope" functions as an adjectival phrase modifying nouns like "calculation", "estimate", or "analysis". According to Ludwig, it describes something done quickly and with simplified assumptions. It characterizes the nature of the calculation rather than performing a grammatical role within a sentence.

Expression frequency: Very common

Frequent in

News & Media

62%

Academia

19%

Science

19%

Less common in

Formal & Business

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

The phrase "back of the envelope" is a common idiom used to describe quick, approximate calculations or estimates. Ludwig AI confirms its correct usage in written English. It functions as an adjectival phrase, typically modifying nouns like "calculation" or "estimate", signaling a simplified approach. While widely used in news and media, and appearing in academic and scientific contexts, it maintains a neutral to informal register. When using this phrase, it's important to acknowledge the limitations of such calculations and avoid presenting them as precise results. Consider alternatives like "rough calculation" or "ballpark figure" for different nuances.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

napkin math

Synonymous and highlights the informality of quick calculations.

rough calculation

Emphasizes the approximate nature of the calculation.

ballpark figure

Focuses on obtaining an estimate within a reasonable range.

quick estimate

Highlights the speed and informality of the estimation.

order-of-magnitude calculation

Suggests an estimation focused on powers of ten.

preliminary assessment

Indicates an initial evaluation, often without detailed analysis.

thumb rule calculation

Emphasizes the use of a practical and approximate method.

crude estimation

Emphasizes the lack of precision in the estimation.

basic arithmetic

Focuses on applying simple mathematical operations for a quick result.

cursory calculation

Indicates a superficial and rapid calculation.

FAQs

How can I use "back of the envelope" in a sentence?

You can use "back of the envelope" to describe a quick, approximate calculation, such as: "Let's do a "quick calculation" to get a sense of the potential costs."

What's a simpler way to say "back of the envelope"?

Simpler alternatives include "rough estimate", "ballpark figure", or "quick calculation".

Is "back of the envelope calculation" formal or informal?

"Back of the envelope calculation" is generally considered an informal expression. Use more formal terms like "preliminary assessment" or "order-of-magnitude calculation" in formal contexts.

When is it appropriate to use a "back of the envelope" calculation?

It's appropriate when you need a fast, high-level estimate and don't require precise results. It's also useful for quickly evaluating the feasibility of an idea or project.