How to use this angle average calculator
Find the mean direction of angles in degrees using circular statistics. Unlike an ordinary arithmetic average, this method handles the wrap between 360° and 0°. Balanced or opposing directions produce an undefined result instead of an arbitrary average direction.
- Enter the angle in degrees values in the labeled fields, using consistent units.
- Load the example to inspect the expected format, then replace it with your own values.
- Select Calculate and check the result alongside its working. Reset starts a fresh calculation.
Angle Average formula
Direction = atan2(Σsin θ, Σcos θ), normalized to [0°, 360°)
The calculation represents each angle as a unit vector, adds the horizontal and vertical components, and uses the direction of the resulting vector. Angles outside one turn are wrapped without changing their direction.
Follow the numbers
350° and 10° point either side of north, so their circular mean is 0°. The ordinary arithmetic mean of 180° points the wrong way.
Load the example above to inspect the entries, then change one value and calculate again. The result follows your selected method. Display rounding changes how the answer is shown; it does not change the underlying observations or weights.
What to check before using the result
Opposite directions such as 0° and 180° cancel. A normalized resultant below 10⁻¹² is treated as ambiguous. All angles here have equal weight.
Keep enough precision in the source values for your task. A result calculated from rounded summaries can only be as precise as those summaries. If a number was mistyped or an observation is missing, correct the inputs and calculate again before copying or exporting the answer.
Choose a related calculator
Common mistakes to avoid
- Confusing a blank with zero. A real zero is an observation. Missing information is not automatically zero.
- Mixing incompatible scales. Use consistent units, or normalize values before combining them.
- Rounding too early. Keep the original values and round at the result stage.
- Using the wrong weighting. Opposite directions such as 0° and 180° cancel. A normalized resultant below 10⁻¹² is treated as ambiguous. All angles here have equal weight.
Frequently asked questions
What formula does this calculator use?
Direction = atan2(Σsin θ, Σcos θ), normalized to [0°, 360°). 350° and 10° point either side of north, so their circular mean is 0°. The ordinary arithmetic mean of 180° points the wrong way.
What should I check about the method?
Opposite directions such as 0° and 180° cancel. A normalized resultant below 10⁻¹² is treated as ambiguous. All angles here have equal weight.
How many entries can I use?
Paste up to 10,000 values, or use up to 100 individual rows when the chosen input method supports them. Numbers must be finite and no greater than 1 trillion in magnitude. Group and old-count inputs have additional whole-number requirements.
Are the displayed decimals exact?
The calculation uses standard floating-point numbers and compensated addition. Results are rounded only for display. Very small values use scientific notation so they do not silently appear as zero. Select the display precision you need, while respecting the accuracy of your original data.
Are my entries saved or sent anywhere?
The calculator performs its arithmetic in your browser. It does not automatically store entries or send them to a server. Copy, print, and CSV actions happen only when you choose them.
Read our calculation methodology for supported precision, validation, and assumptions.