Math & Scientific
Limit Calculator
Limit: limit Calculator estimates the limit numerically by evaluating the expression very close to the target point. Worked through below with real figures, and the calculator repeats the working on your own inputs — free, on-device, instant.
Limit Calculator takes your expression in x and as x → and gives back the result, applying the standard method. It's a quick, browser-based way to work through a calculation.
About this calculator
Limit is easiest to get wrong in the setup, not the arithmetic. Limit Calculator estimates the limit numerically by evaluating the expression very close to the target point. It matters when you need the exact relationship checked quickly rather than worked through by hand. The worked example on this page (lim x→2 (x² − 4)/(x − 2) = lim (x + 2) = 4 (the discontinuity cancels).) shows the full substitution; the calculator above runs the same working on your own numbers, in your browser, with nothing uploaded.
How to use
- Type a function of x, for example (x^2 - 1) / (x - 1).
- Enter the value that x approaches.
- Press Calculate to estimate the limit.
- Read the two-sided limit, or a message if the left and right sides disagree.
Why use Limit Calculator
Fast
Calculations run in your browser. No round trip to a server.
Private
Your inputs never leave your device. Nothing is uploaded.
Free
No signup, no paywall, no ads-in-results, no watermarks.
Accurate
Numerical estimates, with the method shown in each result.
Mobile-ready
Optimised for phones, tablets, and desktops alike.
Transparent
Honest disclaimers wherever browser limits or regional rules apply.
Common uses
Use it when revising for exams
Use it when preparing worksheets
Use it for verifying answers from a textbook
Use it for double-checking a spreadsheet result
Use it for understanding a formula's behaviour
Limit in competitive-exam practice
Technical notes
Limit Calculator estimates the limit numerically by evaluating the expression very close to the target point.
Inputs are taken exactly as entered, so check for typos before trusting an answer.
Results are rounded for display; the underlying calculation keeps full precision.
FAQ
How does it detect a one-sided mismatch?
It samples the function just below and just above the target point. If the left-hand and right-hand estimates differ beyond a small tolerance, it reports that the two-sided limit does not exist.
Does it handle limits that blow up to infinity?
Yes. If the function grows without bound near the point, such as 1/x at 0, the calculator reports that the limit does not exist rather than a finite number.
Is the limit exact?
No. It is a numerical estimate from sampled points, so it is very accurate for well-behaved functions but is not a symbolic limit.
Does the Limit Calculator send my data to a server?
No. The Limit Calculator runs entirely in your browser, so nothing you enter is uploaded, stored, or shared.
Worked example
lim x→2 (x² − 4)/(x − 2) = lim (x + 2) = 4 (the discontinuity cancels).