Weighted Harmonic Mean Calculator
Calculate the weighted harmonic mean as Σw / Σ(w/x).
Open toolCircular Statistics Calculator
Calculate a weighted circular mean, resultant length and circular variance from angles. Provide Angles (degrees), Optional nonnegative weights to compute results directly in your browser. Angles wrap around the circle. Weights must match angle count with a positive total. Mean angle is undefined when resultant length ≤ 1e-12; the tool reports this condition explicitly instead of inventing a direction. 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 Circular Statistics Calculator Works & Core Formula
The Circular Statistics Calculator evaluates Angles (degrees), Optional nonnegative weights in client-side JavaScript using the deterministic rule below and updates the output panel immediately without uploading data to a server.
Calculate a weighted circular mean, resultant length and circular variance from angles.
Angles wrap around the circle. Weights must match angle count with a positive total. Mean angle is undefined when resultant length ≤ 1e-12; the tool reports this condition explicitly instead of inventing a direction. Numeric output uses up to 12 significant digits; floating-point rounding can occur.
Circular Statistics Calculator Quick Reference & Input Guide
Review the input parameters, allowed value ranges, and worked reference cases for the Circular Statistics Calculator below before running your calculation.
| Parameter / Scenario | Default / Sample Value | Rule or Allowed Range | Output / Usage Note |
|---|---|---|---|
| Input: Angles (degrees) | 350,10 | Separate finite decimal values with commas, spaces or newlines; at most 1,000 values, each within ±1e12. | Required workspace parameter |
| Input: Optional nonnegative weights | (User supplied) | Leave empty for equal weights, otherwise one weight per angle. | Required workspace parameter |
| Worked Case 1: Baseline run (Angles (degrees) = 350,10) | Preloaded / test values | Calculate a weighted circular mean, resultant length and circular variance from angles | Angles (degrees) = 350,10; Optional nonnegative weights = . Output: Circular mean: 0 deg; Mean resultant length: 0.984807753012; Circular variance: 0.0151922469878. |
| Worked Case 2: Comparison scenario (circular statistics in r) | Preloaded / test values | Calculate a weighted circular mean, resultant length and circular variance from angles | Angles (degrees) = 0,90; Optional nonnegative weights = 1,1. Output: Circular mean: 45 deg; Mean resultant length: 0.707106781187; Circular variance: 0.292893218813. |
Step-by-Step Guide to Using the Circular Statistics Calculator
Follow these three steps to configure Angles (degrees), Optional nonnegative weights, verify unit and boundary rules, and export your Circular Statistics Calculator output.
Enter the inputs
Start with angles (degrees). Separate finite decimal values with commas, spaces or newlines; at most 1,000 values, each within ±1e12.
Input and settings
Check units and mode
Angles wrap around the circle. Weights must match angle count with a positive total. Mean angle is undefined when resultant length ≤ 1e-12; the tool reports this condition explicitly instead of inventing a direction. 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 Circular Statistics Calculator
These concrete scenarios illustrate how the Circular Statistics Calculator processes baseline inputs, comparison checks, and boundary constraints.
Baseline run (Angles (degrees) = 350,10)
Angles (degrees) = 350,10; Optional nonnegative weights = . Output: Circular mean: 0 deg; Mean resultant length: 0.984807753012; Circular variance: 0.0151922469878.
Comparison scenario (circular statistics in r)
Angles (degrees) = 0,90; Optional nonnegative weights = 1,1. Output: Circular mean: 45 deg; Mean resultant length: 0.707106781187; Circular variance: 0.292893218813.
Boundary & unit check (Circular Statistics Calculator)
When solving for 'circular statistics calculator', verify that Angles (degrees), Optional nonnegative weights use consistent units and stay within the documented scope: Angles wrap around the circle. Weights must match angle count with a positive total. Mean angle is undefined when resultant length ≤ 1e-12; the tool reports this condition explicitly instead of inventing a direction. Numeric output uses up to 12 significant digits; floating-point rounding can occur.
How to Read and Verify the Circular Statistics Calculator Output
The output panel reports the exact result derived from Angles (degrees), Optional nonnegative weights alongside any unit or formatting notes.
Every calculation follows the rule: Calculate a weighted circular mean, resultant length and circular variance from angles. 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 (Angles wrap around the circle. Weights must match angle count with a positive total. Mean angle is undefined when resultant length ≤ 1e-12; the tool reports this condition explicitly instead of inventing a direction. 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 Circular Statistics Calculator output.
Operational scope: Angles wrap around the circle. Weights must match angle count with a positive total. Mean angle is undefined when resultant length ≤ 1e-12; the tool reports this condition explicitly instead of inventing a direction. 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 Circular Statistics Calculator
Answers about using Circular Statistics Calculator and understanding its results.
What formula or rule does the Circular Statistics Calculator use?
The Circular Statistics Calculator applies the rule: Calculate a weighted circular mean, resultant length and circular variance from angles. Enter Angles (degrees), Optional nonnegative weights into the workspace and the tool computes the exact output in your browser.
What input parameters and units are required for Circular Statistics Calculator?
Yes. Provide Angles (degrees), Optional nonnegative weights 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 Circular Statistics Calculator?
Angles wrap around the circle. Weights must match angle count with a positive total. Mean angle is undefined when resultant length ≤ 1e-12; the tool reports this condition explicitly instead of inventing a direction. 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 Circular Statistics Calculator free and does it keep my inputs private?
Yes. All calculations for the Circular Statistics Calculator execute 100% locally in your browser's JavaScript runtime. No inputs or results are uploaded to any external server.
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