Description
Return size, small-angle size/distance radians and exact 2×atan(size/(2×distance)) radians.
A stimulus model relates a chosen level to a supplied response curve, geometry or adaptive rule. One inverse curve or staircase step can be computed without fitting observations, measuring perception or establishing an individual's threshold.
Return size, small-angle size/distance radians and exact 2×atan(size/(2×distance)) radians.
When to use this tool
Use Stimulus Pixel Visual Angle Small Angle Term when you need the stated stimulus-model or adaptive-step calculation.
How to use the tool and how it works
- Enter pixels, millimetersPerPixel, viewingDistanceMm. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read millimeters, approximateRadians, exactRadians. Use the output convention below.
Require nonnegative pixels and positive millimeters/pixel and viewing distance in millimeters. Return size, small-angle size/distance radians and exact 2×atan(size/(2×distance)) radians.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| pixels | Pixels | Required. Finite number; minimum 0. |
| millimetersPerPixel | Millimeters Per Pixel | Required. Finite number; strictly above 0. |
| viewingDistanceMm | Viewing Distance Mm | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| millimeters | Millimeters | Required. Finite number. |
| approximateRadians | Small-angle full extent: size divided by distance. Unit: rad. | Required. Finite number. |
| exactRadians | Full centered angular extent 2·atan(size/(2·distance)). Unit: rad. | Required. Finite number. |
{
"input": {
"pixels": 100,
"millimetersPerPixel": 0.25,
"viewingDistanceMm": 500
},
"output": {
"millimeters": 25,
"approximateRadians": 0.05,
"exactRadians": 0.04998958723784032
}
}Limitations and assumptions
- Angle is the full angular extent under centered flat-target geometry. Small-angle error grows with size/distance; monitor calibration, gaze, perception and clinical significance are not assessed.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Fit and validate the appropriate model on the study data when estimating a threshold. Review lapse/guess assumptions, calibration, convergence, uncertainty and participant context.
References
Similar or alternative tools
- astronomy/angular-size-from-diameter-distance
A planar disk’s angular diameter follows exact tangent geometry at its center distance.
- typography/apparent-size-viewing-distance-points
Apparent printed-letter size is an angle determined by measured ink height and viewing distance.