Small Angle Formula Arcseconds Calculator
Restricted small-anglelinearθarcsec=D/d×206264.80624709636,D/d≤0.1,theoreticalerrornot exactatanor spherearcsin. Actual independent model/unit/frame/epoch/calibration and applicable measurement established;not precise ephemeris,forecast,geodesy operation,identity or safety approval.
Description
The small-angle formula relates a transverse physical size to an angular size when the size-to-distance ratio is small.
The small-angle formula relates a transverse physical size to an angular size when the size-to-distance ratio is small.1
This calculator expresses the first-order approximation in arcseconds and explicitly limits that ratio to 0.1.
When to use Small Angle Formula Arcseconds Calculator
Use this tool to apply the stated small angle formula arcseconds calculator operation with an explicit input and unit basis.
How to use Small Angle Formula Arcseconds Calculator and how it works
- Establish the measurement basis and units described above.
- Enter actualTransverseDiameter, actualDistance and run the tool.
- Read result.value using the output meanings below.
- If input is rejected, correct the stated type, range, ordering or alignment issue and rerun; review successful results under the declared convention.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| actualTransverseDiameter | Transverse Diameter. Units, ordering and applicable branch are specified in the algorithm. | number | required; finite; nonnegative; further conditions in the algorithm |
| actualDistance | Distance. Units, ordering and applicable branch are specified in the algorithm. | number | required; finite; strictly positive; further conditions in the algorithm |
Require nonnegative diameter, positive distance in the same unit and diameter/distance no greater than 0.1. Multiply the ratio by 206264.80624709636; this approximation is different from an exact disk or spherical-limb angle.
angularSizeArcsec ≈ 206264.80624709636 × diameter/distance Apply the declared units, ordering and branch conditions.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the declared output fields. | object |
| result.value | First-order angular size in arcseconds. | number |
{
"input": {
"actualTransverseDiameter": 1,
"actualDistance": 1000
},
"output": {
"result": {
"value": 206.26480624709637
}
}
}Limitations and assumptions
The output applies the declared operation to the values you supply. Establish the measurement basis, units, coefficients and any caller-selected rules before interpreting it. The tool does not independently collect or verify observations or decide whether a model or reference applies.
Supply explicit required fields with the documented types and dense aligned arrays. Unknown fields, wrong types and nonfinite numbers are rejected. Branch-specific constraints are explained above. A returned boolean, signed difference or tied result follows the stated convention; an input error instead means the required input contract was not satisfied. Very large inputs or outputs may be rejected by shared resource limits.
Alternative or Complementary methods
For a related operation, use Star Trail Length Pixels Per Minute. A stationary camera records star motion caused by Earth’s sidereal rotation.
For a related operation, use Angular Size From Diameter and Distance. A planar disk’s angular diameter follows exact tangent geometry at its center distance.
References
Similar or alternative tools
- Star Trail Length Pixels Per Minute
A stationary camera records star motion caused by Earth’s sidereal rotation.
- Angular Size From Diameter and Distance
A planar disk’s angular diameter follows exact tangent geometry at its center distance.