ERR:DOMAIN means you fed a function an input outside the range it's allowed to accept. The command itself is fine and your syntax is fine — the number you gave it is impossible for that function. Once you know the handful of functions that trigger it, the fix is usually a ten-second correction.
What just happened
Every function has a set of legal inputs — its domain. Ask for the inverse sine of 2, and there's no answer: no angle has a sine of 2. Instead of guessing, the TI-84 stops and shows ERR:DOMAIN with the usual two options, 1: Quit and 2: Goto. Choose 2: Goto and the cursor jumps to the command that failed, so you can see exactly which input to re-check.
The usual suspects
| Function | Legal input | Common mistake |
|---|---|---|
sin⁻¹( , cos⁻¹( | Values from −1 to 1 | Taking the inverse sine of something like 1.5 or 2 |
invNorm( | Probability strictly between 0 and 1 | Typing 95 instead of 0.95 |
log( , ln( , √( | Non-negative (positive for logs) in Real mode | A negative number sneaking in mid-formula |
! (factorial) | Not defined for negatives or arbitrary non-integers | Taking the factorial of a negative or non-integer value |
The AP Stats classic: invNorm(95)
If you're in AP Statistics, this is almost certainly your error. invNorm( takes a probability, and probabilities live strictly between 0 and 1. Entering a probability that's 0 or less, or 1 or more, triggers ERR:DOMAIN instantly.
The mistake everyone makes: the problem says "the 95th percentile," so you type invNorm(95). But 95 isn't a probability — 0.95 is.
- Wrong:
invNorm(95)→ ERR:DOMAIN - Right:
invNorm(0.95)→ about 1.645
Same deal with invNorm(90), invNorm(99), and friends. Convert the percent to a decimal every time. For a full walkthrough of normalcdf( and invNorm( — including where the menus are and which argument goes where — see /guides/normalcdf-invnorm/.
Inverse trig: stay inside [−1, 1]
sin⁻¹( and cos⁻¹( only accept values from −1 to 1, because sine and cosine themselves never leave that range. If you're solving a triangle and get ERR:DOMAIN on an inverse trig function, the value you're feeding it is bigger than 1 (or smaller than −1). That usually means an earlier arithmetic step is off — a ratio got flipped, or a side length got swapped. Re-derive the ratio before blaming the calculator.
Logs and square roots of negatives
In Real mode, log(, ln(, and √( reject negative inputs. If you hit ERR:DOMAIN here mid-formula, some intermediate value went negative when you expected it positive. Choose 2: Goto, look at the expression, and evaluate the inside part by itself on the home screen to see what value is actually reaching the function.
The fix, in general
- Choose
2: Gototo land on the failing command. - Identify which function it is (inverse trig,
invNorm(, log, root, factorial). - Check its input against the legal range in the table above.
- Correct the value — most often, converting a percent like 95 to the decimal 0.95, or fixing an earlier step that produced an out-of-range number.
If your error message says something else — SYNTAX, INVALID DIM, DIM MISMATCH — it's a different problem with a different fix. The overview at /error-fixes/error-messages/ sorts them all out.
Try the fix right now
Don't wait for the next quiz to find out whether you've got it. Open the free online TI-84 calculator — a TI-84 Plus CE in your browser, no download — and try invNorm(95) to see the error, then invNorm(0.95) to see it work. Thirty seconds of practice now and ERR:DOMAIN will never slow you down again.