TL;DR: To get infinity on a calculator, divide any non-zero number by zero. Most calculators will show Error, Cannot divide by zero, or Math ERROR rather than the ∞ symbol, because the operation is undefined rather than infinite. The exceptions are graphing calculators and some scientific models, which display ∞ in certain contexts, and the overflow case: a number too large for the display shows 1E99 or OVERFLOW, not infinity.
What dividing by zero actually does
The instinct is to expect infinity, and that is mathematically reasonable in one specific sense: as a divisor approaches zero, the quotient grows without bound. But a calculator does not evaluate limits; it evaluates a single operation, and division by zero has no result in the number system it works in.
So the honest answer is that the operation is undefined. Whether the device displays an error, infinity, or something else is a design decision, not a mathematical one.
That explains why the same input produces three different screens across three calculators, and why “how do I get infinity” has no single answer.
What each platform shows
The behaviour differs by device family, and knowing which you have tells you what to expect.
Basic four-function calculators. Display E, Error, or nothing at all, and often lock until cleared. Some cheaper models simply reset to zero.
Scientific calculators. Typically show Math ERROR or Cannot divide by zero. Texas Instruments models generally error; some Casio models will display an infinity symbol in complex or calculus contexts.
Graphing calculators. The most likely to display ∞, particularly in limit, integral, and sequence contexts where infinity is a legitimate value rather than an error.
Phone and web calculator apps. Usually show “Cannot divide by zero” or a generic error, because the underlying implementation raises an exception that the interface catches.
If a specific model is the goal, the reliable method is to check its manual for the error table rather than trying inputs at random.
Infinity versus overflow
These get conflated constantly and they are different situations.
Infinity would be the result of a genuine infinite quantity. It has no finite digit representation.
Overflow happens when a result exceeds the largest number the device can hold. A calculator with 10 display digits and a two-digit exponent tops out around 9.99 × 10^99. Computing 10^100 exceeds that, and the device reports overflow or shows 1E99.
Overflow is a storage limit; infinity is a mathematical concept. A calculator showing 1E99 is telling you the number is too big to represent, not that it is infinite. Typing 10^500 will not produce ∞ on a device that caps at 10^99.
The tricks people use
Several of the “infinity” tricks that circulate are exploiting different things, and it is worth separating them.
Division by zero produces an error on most devices, and a symbol on a few. This is the one that sometimes works.
Tangent of 90 degrees. The tangent function grows without bound as the angle approaches 90 degrees from below, so tan(90) is undefined. Some calculators return a very large number due to how the angle is approximated in radians, others error. Anything returned is a rounding artefact, not infinity.
Repeated squaring. Squaring repeatedly until the result overflows produces overflow, not infinity, and the display will say so.
Logarithm of zero. Undefined, and errors on nearly every device.
The pattern is consistent: where the device shows a special symbol, it is because the software has a representation for that case. Where it errors, there is no such representation.
Why this matters beyond the trick
The reason to care is that error handling tells you how much the device is doing for you.
A calculator that silently returns zero for division by zero is dangerous, because the wrong answer propagates. One that errors forces you to notice. That distinction is why engineering calculators are conservative about returning values in undefined cases, and why spreadsheets — which famously propagate error values visibly — are considered safer for audit trails.
In exams, the same issue appears as a grading problem: a student who divides by zero and writes down whatever appeared on screen has recorded an error as a result. Understanding that the display is a design choice, not a mathematical answer, is the actual lesson.
Getting a genuine infinite result
If the goal is to see infinity handled properly, the context has to be one where it is a legitimate value rather than a failure.
Limits are the clearest case: a limit expression that diverges returns infinity as a symbol on a graphing calculator, because the result of a limit genuinely can be infinite. Summation to infinity in a series, and improper integrals, behave the same way.
Outside those contexts, there is no correct way for a calculator to display infinity, because the computation has no result. That is the underlying answer to the question, and it is more interesting than the trick itself.
The short version
Divide by zero to attempt it. Most devices error, graphing calculators may show ∞, and anything that shows 1E99 is reporting overflow rather than infinity. The display is a design decision; the mathematics says undefined.
If you are testing how a particular engine handles edge cases, an online calculator with visible settings makes the difference between an error and a returned value easier to study than a sealed device does.
