ERR: DOMAIN on TI-84 — What It Means and How to Fix It

When a TI-84 shows ERR: DOMAIN, the expression on the screen was read perfectly well — the calculator simply cannot produce a real answer from the numbers it was handed. Every function accepts only certain inputs, and this message means that one of yours falls outside that set.

That distinction shapes the fix. ERR: DOMAIN is a problem with a value, not with punctuation, and it comes from a short list of situations: a denominator that reached zero, an argument to a logarithm or a square root that the real numbers do not allow, a trigonometric ratio that cannot exist, or a data set that does not suit the regression model you chose.

Because the message looks alarming and the screen marks no obvious culprit, students often start the whole calculation again. Finding the single offending value is usually faster than the original calculation took.

What ERR: DOMAIN means on a TI-84

The domain of a function is the complete set of inputs for which that function is defined. ln(x) is defined for positive x only. sin⁻¹(x) is defined only when x sits between −1 and 1. Division by zero is not defined at all. Hand one of these operations a value outside its domain and the calculator declines rather than returning a number that looks plausible but is not.

Choosing 1:Quit returns you to the home screen with the expression still on the line, so you can edit it. Choosing 2:Goto moves the cursor to the argument the calculator rejected. On a short expression either choice is fine; on a long one, 2:Goto saves a great deal of reading. Graphs are the exception to the rule: the TI-84 Plus CE allows undefined values while plotting, so a curve breaks instead of raising an error, which is why a function can look continuous on screen and still fail when evaluated.

The causes, in the order they are worth checking

A trigonometric ratio that cannot exist

sin⁻¹(2) and cos⁻¹(1.5) have no real answer, because the sine and cosine of a real angle never leave the interval from −1 to 1. The calculator reports ERR: DOMAIN in either RADIAN or DEGREE mode, since the restriction belongs to the function rather than to the angle unit. If the ratio came from an earlier calculation, round it or reconsider the geometry that produced it.

A logarithm of zero, or of a negative value in Real mode

ln(0) and log(0) are undefined, and ERR: DOMAIN is the result. A negative argument is a slightly different case: the true answer is complex, and in Real mode the TI-84 Plus family reports ERR: NONREAL ANS instead. The two messages describe the same underlying problem and are fixed in the same way — change the input, or allow complex results. Logarithmic scales in science data are a common source, so it is worth checking whether the smallest value in the data set is genuinely positive.

A division by zero

1/0 is the simplest trigger. Recent OS versions of the TI-84 Plus CE name this case separately as ERR: DIVIDE BY 0, while other versions fold it into ERR: DOMAIN. Whichever label appears, a denominator reached zero somewhere. Dividing by a variable hides the problem, because the value that reaches zero is produced by the calculation rather than typed by you.

A table or a zoom that evaluates a division by zero

Set Y1 to 1/(X−2) and generate a table beginning at TblStart 2, and the calculator is asked for a value it cannot represent. A table cell has no way to be left empty, so the evaluation stops with ERR: DOMAIN. Our guide to the table feature explains how TblStart and ΔTbl decide which x-values are tested, which is how you find the offending row quickly.

Regression data outside the model’s domain

This cause is documented by TI and it surprises students who assume the command must be at fault. A logarithmic regression such as LnReg needs positive x-values, an exponential regression needs positive y-values, and a power regression needs positive x-values, because each model takes a logarithm of the data before fitting the line. A single stray zero left in a list is enough to trigger the message. The linear regression walkthrough shows the list-editing habits that keep regressions clean.

Using 2:Goto to identify the offending value

Press 2 on the error menu and the cursor jumps to the argument the calculator could not use. On a one-line expression that is decisive: you see at once whether the fault is a single value or a whole sub-expression.

On a multi-line command the jump is less helpful. LnReg L1,L2 is evaluated as a single instruction, so 2:Goto may land on the command itself rather than on the row that is wrong. In that situation press STAT and choose 1:Edit, then read the two lists side by side looking for a zero or a negative value in the list the chosen model cannot accept. On the TI-84 Plus CE, scrolling to the bottom of a list also confirms whether a stray entry has extended it beyond your real data.

When the answer is meant to be complex

If the complex answer is what you actually want, the repair is a MODE setting rather than a change to the maths:

1. Press MODE.
2. Use the arrow keys to reach the line that currently reads REAL.
3. Move right onto a+bi and press ENTER.
4. Leave the menu with 2nd MODE.

Students working with complex numbers, or on precalculus and engineering material, usually want a+bi left on. Students who never need complex answers are better served by Real mode, because an unexpected i in an answer is easier to miss than a clear error message.

Deciding whether the maths or the typing is at fault

Three questions settle the question quickly.

• Is the value inside the domain of the function you used? If the answer is no, the fault is mathematical, and the honest response is to reconsider the problem rather than to force the calculator.
• Did you intend a complex answer? If you did, change MODE once and the same keystrokes will work for the rest of the session.
• Is the data correct? Regressions fail on data that the model cannot accept, so check the lists before checking the command.

If the input is legitimate and the message still appears, re-read the line the way you would for a punctuation fault, using the method on our ERR: SYNTAX page. An unclosed bracket changes which value is passed to a function, so a number that is valid on its own can become invalid once it sits inside the wrong call.

Worked example: a logarithmic regression with a zero in the list

Suppose L1 holds {0, 1, 2, 4} and L2 holds {1, 3, 4, 6}, and you run STAT ▸ CALC ▸ 9:LnReg.

The model is y = a + b·ln(x), and ln(0) has no value, so the calculation stops before it reaches the fit. Choosing 2:Goto returns you to the command rather than to the list, which is why the fastest repair is to open the list editor and delete the row holding the zero.

Removing that row and running LnReg again produces a fit. If the point genuinely belongs in the analysis, choose a model that does not take a logarithm, such as 4:LinReg(ax+b), rather than forcing a model that the data cannot support.

After you correct the value

If the message changes after your edit, that is useful information rather than a new problem. ERR: BOUND means a numeric search was given an interval it cannot work with, and ERR: SYNTAX means the punctuation has now become the issue. Our complete list of TI-84 error codes covers the remaining messages in one table.

Graphing calculators such as the TI-84 Plus and TI-84 Plus CE are permitted on the SAT maths questions and on the AP exams that allow a calculator, but the rules are revised from time to time, so confirm the current wording with the official board and your teacher before test day.