Enter your IPD and target distance to begin. Switch modes for reverse calculations anytime here. See results instantly, then save them as files today.
The convergence angle is the angle between the two sight lines from each eye to a single target point. With IPD as interpupillary distance and d as target distance:
| IPD (mm) | Distance (m) | Angle (deg) | Notes |
|---|---|---|---|
| 63 | 0.40 | 9.0055 | Typical near viewing distance. |
| 64 | 1.00 | 3.6657 | Moderate distance target. |
| 60 | 0.30 | 11.4212 | Closer target increases convergence. |
| 70 | 2.00 | 2.0051 | Farther targets reduce convergence angle. |
The angle of convergence is the angle between both lines of sight when your eyes focus on one point. It depends on your interpupillary distance (IPD) and the target distance. Larger IPD or shorter distance increases the angle, while farther targets reduce it.
Many adults have an IPD between 54–74 mm, with a common mid value around 63 mm. At a 0.40 m viewing distance, an IPD near 63 mm produces an angle near 9.01°. At 1.00 m, the same order of IPD yields angles around 3–4°.
The formula uses a ratio of lengths, so units must match. This tool converts IPD and distance to meters, computes with radians internally, and then converts to your chosen output unit. This reduces mistakes when mixing millimeters, inches, feet, or centimeters.
If you know your IPD and can estimate a comfortable convergence angle, you can back-calculate the distance. For example, a smaller angle generally corresponds to a farther target. The distance mode uses d = (IPD/2) / tan(θ/2).
If you are modeling binocular geometry for a device or simulation, you may know the distance and desired angle, and want the implied IPD. The calculator uses IPD = 2 × d × tan(θ/2). This can help with camera rigs or stereo render setups.
For very small angles, tan(θ/2) becomes tiny, which can produce extremely large distances. That is why the calculator warns when θ is too small for stable distance estimates. Increase precision if you are working near the limits.
Use realistic inputs: IPD around 60–70 mm, and distances between 0.25–2.00 m for common viewing. Compare your result with the example table to spot typos. Turning on steps also shows conversions and substitutions for verification.
After calculation, download CSV to store inputs and outputs in a spreadsheet. For a clean report, use the PDF option, which opens a printable view you can save from your browser. This is useful for lab notes, training logs, or project documentation.
Vergence commonly refers to the inward rotation needed to fixate a target. This calculator returns the total angle between both sight lines, which is directly derived from IPD and viewing distance.
Use your measured interpupillary distance if available. If not, a typical adult value is around 63 mm. Small changes in IPD slightly change the angle, especially at close distances.
Enter the straight-line distance from the midpoint between your eyes to the target point. For reading, 0.30–0.45 m is common; for a monitor, 0.50–0.80 m is typical.
When the angle approaches zero, tan(θ/2) approaches zero, and the computed distance grows very large. That makes results highly sensitive to rounding and measurement noise.
Degrees are easier for most users, while radians are common in engineering and programming. The calculator converts internally, so you can enter and output in the unit you prefer.
Yes. The same geometry applies to two viewpoints converging on a target. Use the IPD mode to explore what separation is implied by a distance and convergence angle in your scene setup.
Accuracy mainly depends on input accuracy and unit selection. The math uses standard trigonometry and double precision. Increase decimal precision and enable steps when you need auditable calculations.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.