My wife heard a guy on the radio say “inter-PO-late” (with penultimate stress), and said “That’s not right, is it?” I said no, I didn’t think so, but (having long since learned not to trust my first reactions) I went off to make sure. Turned out I was right, officially the word only has antepenultimate stress (/ɪn.ˈtɜɹ.pə.ˌleɪt/, in-TER-polate), but I was a bit taken aback by the variety of ways it’s used. AHD:

1. To insert or introduce between other elements or parts.
    a. To insert (material) into a text.
    b. To insert into a conversation. See Synonyms at introduce.
3. To change or falsify (a text) by introducing new or incorrect material.
4. Mathematics
    a. To estimate a value of (a function or series) between two known values.
    b. To create a continuous function that incorporates (a finite set of data), such as creating a curve that passes through a fixed set of points or a surface through a fixed set of curves.
5. To introduce estimated values of (pixel data) into a pixel array to improve the quality of an enlarged digital image.

The OED (entry from 1900) begins with “To polish or furbish up; to put a fresh gloss on. Obsolete”; this reflects the etymology (AHD again):

[Latin interpolāre, interpolāt-, to touch up, refurbish, from interpolis, refurbished; see pel-⁵ in the Appendix of Indo-European roots.]

The Russian equivalent is интерполировать; it appears to have been introduced by Chebyshev (of the many spellings; see The Thread) in the 1850s as a mathematical term and to have spread slowly into other realms: circa 1918 Sukhanov puts it in quotes (“Сознание его успеха распространялось, «интерполировалось» и на его результаты”) and Remizov explains the noun интерполяция ‘interpolation’ in parentheses (“А правда, в этой сказке, говоря по-ученому, амплификаций (распространение) и интерполяций (вставка) незначительно, но это ничего не значит, все по качеству матерьяла”). In his 1926 anthroposophical/Marxist novel Moskva [Moscow], Andrei Bely has the following exchange:

“You don’t know how to interpolate, my good man.”
“No, sir!” The student became confused.
“Interpolate” — he slapped his knee and pounded out his words nasally — “what does that mean?”
And he prompted the answer himself: “It means to insert an intermediate term in a row of other, already known, data: well, sir…”

― Вы не умеете, сударь мой, интерполировать.
― Нет-с! Студент путался.
― Интерполировать, ― шлепал себя по колену рукой и долбился словами и носом, ― что значит?
И — сам же подсказывал:
— Значит ― включать промежуточный член в ряд других, уже данных, известных: ну – вот-с…

After that it seems to be well enough known not to call for explanations. (Incidentally, when I looked at the word in Russian I immediately thought of Интерпол [Interpol], which turns up fairly often in the Corpus results for интерпол*; as far as I remember, that association never once occurred to me in connection with the English word.)

There is also a verb interpellate “to question (someone, such as a foreign minister) formally concerning an official action or policy or personal conduct,” which can be pronounced with either antepenultimate (ɪnˈtəːpɪleɪt) or penultimate (/ɪntəˈpɛleɪt/) stress (if I ever had occasion to say it I would use the latter to avoid confusion), but it’s hardly ever used and would just confuse the issue, so I won’t even mention it here.


  1. Which sense of interpolate are you more used to? I’m most used to interpolate in the sense of making a guesstimate. I’m not sure which number that is on the list. As for interpellate, I’m more used to the noun, interpellation. It’s one of those political words that you see in the news now and then, and it takes a few seconds to realize that it refers to questioning someone, but more formally. (Similar to interrogate, perhaps?)

  2. Which sense of interpolate are you more used to?

    I guess 2.a. (To insert (material) into a text).

    I’m most used to interpolate in the sense of making a guesstimate. I’m not sure which number that is on the list.

    It’s not on the list, which suggests it’s a recent development. Anybody know more about it?

  3. George Grade says

    In math, “interpolate” is often used in contrast to “extrapolate”. You’re interpolating when you have a bunch of data over a certain range, and you estimate a value within that range, but you’re extrapolating when you are estimating a value outside that range. For example, if you have a bunch of heights between 5 feet and 6 feet tall, with associated weights, you’re interpolating if you’re estimating a weight for someone who is 5 foot 6, but extrapolating if you’re estimating a weight for someone who is 7 feet tall. I’ve not heard it used for bare guesstimates, but rather it’s used when following some sort of algorithm (whether good or bad). In general, interpolation is considered a much safer procedure than extrapolating.

  4. I would write term rather than member for член in the Bely excerpt.

    Anybody know more about it?

    I would guess it’s an interpretation of 4a, which contrasts with extrapolate. You extrapolate when the new example is outside the range of data that’s already known (which requires more guesswork) and interpolate when it’s in that range.

    @George: jinx!

  5. I would write term rather than member for член in the Bely excerpt.

    Yes, sloppy of me — fixed, thanks.

  6. I first met “interpolate” in mathematics, long after meeting “extrapolate” in general reading. I therefore assumed “interpolate” was coined on the model of “extrapolate”, when in fact it was the other way around. None of the AHD senses seem to have drifted too far from sense 4 (not so OED sense 1, mind).

    The pronunciation of “Interpol” does vary: for the final vowel, America has GOAT, England LOT. (Do the Scots have GOAT in Interpol? GOAT in police~polis is at least as common there as in the US.)

  7. The “guesstimate” meaning is an extrapolation of interpolation.

    (Smart-ass, at your service.)

  8. 1. On the correct pronunciation of “interpolate,”

    2. “Interpellate” may be “hardly ever used” (hat) in general, but the term and the idea are specifically influential in Marxist theory. See

  9. David Eddyshaw says

    Diolch, JM. Interesting link.

    According to Althusser, schools are a particularly important ISA because teachers hold captive the undivided attention of their students

    suggests a certain (how shall I put this?) otherworldliness on the part of Althusser … “school” here is (one supposes) an École normale supérieure (perhaps) rather than some less Olympian institution.

    Still, Hegemony is indeed where it’s at. As we see all about us, alas.

  10. Oh. I’m sure I use interpolate, extrapolate, deviate, estimate, evaluate, calculate all wity the same final syllable stress.

  11. @Dmitry Pruss: I think standard English has primary antepenultimate stress in all those words, with secondary final stress (no vowel reduction).

  12. I was familiar with (1)-(4) but not (5) – I must have seen “interpolate” on image editor menus but didn’t pay much attention. On the other hand, was it really necessary to include (5) as a separate high-level meaning? Wouldn’t it be covered by (4) and merit – at most – being glossed as (4c)? Likewise, (3) is a subcase of (2a), logically speaking. I guess being used as trade jargon is grounds for promotion.

    The 1900 OED deffo came as a total surprise to me, though.

  13. On the other hand, was it really necessary to include (5) as a separate high-level meaning? Wouldn’t it be covered by (4) and merit – at most – being glossed as (4c)?

    No, it’s clearly a separate specialized meaning, even if it historically developed from (4).

  14. Stressed final -ate is common in Irish English

  15. Interesting that Chebyshev played a role in establishing a sense of ‘interpolation’. ‘Chebyshev interpolation’ is an important approximation technique (using Chebyshev polynomials) that obeys a particular optimality constraint– the approximation has minimal maximum error. I didn’t suspect that the criterion went back to Chebyshev himself.

  16. Like Alex K., I was surprised to see definition 5 listed as a new main sense. In graduate school, I spent a lot of time on computer graphics, including doing publishing layout jobs for extra money. So sense 5 (along with lots of much more technical vocabulary, like for the algorithms used to doing the interpolation, such as bicubic resampling) was very familiar to me, but I only thought of it as a specific example of sense 4.

    I suppose that it might make a difference if there were a body of people using sense 5, while lacking detailed familiarity with sense 4. Everyone around me (at the MIT student newspaper) when I was learning this stuff was totally familiar with the mathematical usage of interpolation, but other people coming to computer graphics with different backgrounds might not be.

  17. For me, the verb estimate has has almost equal stress on the first and last syllables (as best I can tell, anyway), but as a noun the last vowel is a schwa.

    I know interpolate mainly in the mathematical sense, and that’s probably where I first encountered it. The first two senses are unfamiliar to me. I would probably just use insert or, if I wanted to show off, intercalate (which also has a scientific meaning, typically in the sense of additional atoms intercalated into a crystal lattice).

  18. Heh. To me, intercalate means only “interpolate (an intercalary period) in a calendar.”

  19. Another case of a calendrical/religious term being adopted into the scientific vocabulary, along with canonical and secular.

  20. @David L: For me (and most standard speakers, I think), estimate has a stress difference between the noun and verb. Both have primary initial stress, but only the noun has the pronunciation you describe, with the final vowel reduced to a schwa. The same change exists for advocate, deviate, and separate It appears to be a regular phenomenon, a trisyllabic version of the usual tendency for verb-derived nouns in English to get initial stress. (Most other common words of more than two syllables with the niun/verb stress shift have a two-syllable prefix, like inter-, over-, or under-, and final main stress in the verb form.)

  21. My wife and I use Rotten Tomatoes to avoid wasting time on bad movies. I take delight in calling their index of reviews the tomaTOMeter.

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