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
This tool checks nearby numerical values. For (x^2 - 4)/(x - 2) as x approaches2, the samples approach4. The separate algebraic explanation factors the numerator and cancels x - 2 for x unequal to2; the form does not perform that symbolic cancellation.
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 numerical estimate and the final sampled values, or an explanation that the sample is inconclusive.
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
This numerical check samples x at fixed distances from 0.1 down to 0.0000001 on both sides of the target. It compares the final three finite samples using a tolerance of 0.001 × (1 + the final value’s magnitude), then compares the two sides. A stable estimate is not a proof that a mathematical limit exists. An inconclusive result does not prove divergence or nonexistence. Large finite values are not automatically unbounded, and targets too large to represent distinct nearby sample points are rejected. Use analytic reasoning for oscillations, domain boundaries and sensitive cases.
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?
The tool may report that its samples do not produce a common numerical estimate. It cannot prove that a limit fails to exist or determine a symbolic infinite limit; inspect the function and its domain analytically.
Does it handle limits that blow up to infinity?
The tool may report that its samples do not produce a common numerical estimate. It cannot prove that a limit fails to exist or determine a symbolic infinite limit; inspect the function and its domain analytically.
Is the limit exact?
No. It is a numerical estimate from finitely many sampled points. Accuracy depends on the function, the sampling distances and floating-point rounding; analytic reasoning is needed to establish the actual 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).