Digit Preference Analyzer
Count terminal digits and round last-place multiples at an explicitly stated measurement precision.
Open toolBenford Law Analyzer
Count first significant digits and compare them with Benford expected counts. Provide Positive observations to compute results directly in your browser. Only finite positive observations are accepted. Expected digit proportion = log10(1 + 1/d). The chart shows observed counts. Benford comparison alone is not evidence of fraud and is unsuitable for many bounded or assigned-number datasets. Numeric output uses up to 12 significant digits; floating-point rounding can occur.
Free to useNo sign-upRuns in your browser
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Enter the inputs, then select Calculate.
Your result
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Result will appear here
How the Benford Law Analyzer Works & Core Formula
The Benford Law Analyzer evaluates Positive observations in client-side JavaScript using the deterministic rule below and updates the output panel immediately without uploading data to a server.
Count first significant digits and compare them with Benford expected counts.
Only finite positive observations are accepted. Expected digit proportion = log10(1 + 1/d). The chart shows observed counts. Benford comparison alone is not evidence of fraud and is unsuitable for many bounded or assigned-number datasets. Numeric output uses up to 12 significant digits; floating-point rounding can occur.
Benford Law Analyzer Quick Reference & Input Guide
Review the input parameters, allowed value ranges, and worked reference cases for the Benford Law Analyzer below before running your calculation.
| Parameter / Scenario | Default / Sample Value | Rule or Allowed Range | Output / Usage Note |
|---|---|---|---|
| Input: Positive observations | 12,15,27,31,42,58,63,77,89,95 | Separate finite decimal values with commas, spaces or newlines; at most 1,000 values, each within ±1e12. | Required workspace parameter |
| Worked Case 1: Baseline run (Positive observations = 12,15,27,31,42,58,) | Preloaded / test values | Count first significant digits and compare them with Benford expected counts | Positive observations = 12,15,27,31,42,58,63,77,89,95. Output excerpt: Observation count: 10; 1 observed / expected: 2 / 3.01029995664; 2 observed / expected: 1 / 1.76091259056; 3 observed / expected: 1 / 1.24938736608. |
| Worked Case 2: Comparison scenario (Comparison positive observations check) | Preloaded / test values | Count first significant digits and compare them with Benford expected counts | Positive observations = 1,10,100,2,20,3,0.04. Output excerpt: Observation count: 7; 1 observed / expected: 3 / 2.10720996965; 2 observed / expected: 2 / 1.23263881339; 3 observed / expected: 1 / 0.874571156258. |
Step-by-Step Guide to Using the Benford Law Analyzer
Follow these three steps to configure Positive observations, verify unit and boundary rules, and export your Benford Law Analyzer output.
Enter the inputs
Start with positive observations. Separate finite decimal values with commas, spaces or newlines; at most 1,000 values, each within ±1e12.
Input and settings
Check units and mode
Only finite positive observations are accepted. Expected digit proportion = log10(1 + 1/d). The chart shows observed counts. Benford comparison alone is not evidence of fraud and is unsuitable for many bounded or assigned-number datasets. Numeric output uses up to 12 significant digits; floating-point rounding can occur.
Tool result
Calculate and save
Select Calculate, check the labelled result, then use Copy result or Download result.txt.
Review the details
Practical Worked Examples for Benford Law Analyzer
These concrete scenarios illustrate how the Benford Law Analyzer processes baseline inputs, comparison checks, and boundary constraints.
Baseline run (Positive observations = 12,15,27,31,42,58,)
Positive observations = 12,15,27,31,42,58,63,77,89,95. Output excerpt: Observation count: 10; 1 observed / expected: 2 / 3.01029995664; 2 observed / expected: 1 / 1.76091259056; 3 observed / expected: 1 / 1.24938736608.
Comparison scenario (Comparison positive observations check)
Positive observations = 1,10,100,2,20,3,0.04. Output excerpt: Observation count: 7; 1 observed / expected: 3 / 2.10720996965; 2 observed / expected: 2 / 1.23263881339; 3 observed / expected: 1 / 0.874571156258.
Boundary & unit check (Benford Law Analyzer)
When solving for 'benford law analyzer', verify that Positive observations use consistent units and stay within the documented scope: Only finite positive observations are accepted. Expected digit proportion = log10(1 + 1/d). The chart shows observed counts. Benford comparison alone is not evidence of fraud and is unsuitable for many bounded or assigned-number datasets. Numeric output uses up to 12 significant digits; floating-point rounding can occur.
How to Read and Verify the Benford Law Analyzer Output
The output panel reports the exact result derived from Positive observations alongside any unit or formatting notes.
Every calculation follows the rule: Count first significant digits and compare them with Benford expected counts. Because JavaScript uses IEEE 754 double-precision floating-point arithmetic, numeric outputs display up to 12 significant digits where applicable.
Always cross-check the displayed result against the scope note (Only finite positive observations are accepted. Expected digit proportion = log10(1 + 1/d). The chart shows observed counts. Benford comparison alone is not evidence of fraud and is unsuitable for many bounded or assigned-number datasets. Numeric output uses up to 12 significant digits; floating-point rounding can occur) before applying the value to production specifications, financial models, or lab records.
Scope Limits, Accuracy Assumptions & Related Everyday Math Tools
Review these boundary constraints and validation rules before relying on the Benford Law Analyzer output.
Operational scope: Only finite positive observations are accepted. Expected digit proportion = log10(1 + 1/d). The chart shows observed counts. Benford comparison alone is not evidence of fraud and is unsuitable for many bounded or assigned-number datasets. Numeric output uses up to 12 significant digits; floating-point rounding can occur. Inputs that violate minimum/maximum bounds or required format rules are rejected with a clear diagnostic prompt.
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Open toolFrequently Asked Questions About Benford Law Analyzer
Answers about using Benford Law Analyzer and understanding its results.
What formula or rule does the Benford Law Analyzer use?
The Benford Law Analyzer applies the rule: Count first significant digits and compare them with Benford expected counts. Enter Positive observations into the workspace and the tool computes the exact output in your browser.
What input parameters and units are required for Benford Law Analyzer?
Yes. Provide Positive observations using the documented units and format shown in the quick reference table above. Preloaded default values let you test the workflow immediately.
What are the accuracy limits and boundary assumptions for Benford Law Analyzer?
Only finite positive observations are accepted. Expected digit proportion = log10(1 + 1/d). The chart shows observed counts. Benford comparison alone is not evidence of fraud and is unsuitable for many bounded or assigned-number datasets. Numeric output uses up to 12 significant digits; floating-point rounding can occur. Confirm that your inputs fall within the allowed ranges before exporting the result.
Is the Benford Law Analyzer free and does it keep my inputs private?
Yes. All calculations for the Benford Law Analyzer execute 100% locally in your browser's JavaScript runtime. No inputs or results are uploaded to any external server.
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