Lognormal Distribution Calculator
Evaluate lognormal probabilities and arithmetic moments using mean and SD of natural logarithms.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Standardize the natural logarithm of the query, then distinguish arithmetic mean from the log-location and median.
CDF=Φ((ln x−μ)/σ); mean=exp(μ+σ²/2); median=exp(μ)
Worked example
μ=0 and σ=0.5 give median 1, mean exp(0.125)≈1.13314845 and probability 0.5 below x=1.
Assumptions and input details
μ and σ describe natural logs, not arithmetic observations. Positive support only; no parameter fitting, extreme-tail accuracy guarantee or financial return assumption.
References: NIST: probability distributions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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