Advanced Calibration Inputs
Formula Used
Z = H × fy ÷ hpx
fx = fmm × image width ÷ sensor width
fy = fmm × image height ÷ sensor height
fpx = reference pixels × reference distance ÷ reference size
distance = √(tx² + ty² + tz²)
The calculator uses the pinhole camera model. Z is depth along the camera axis. W and H are real marker sizes. wpx and hpx are measured pixel sizes. fx and fy are focal lengths from the calibrated camera matrix. The translation vector formula supports pose results from solvePnP.
How to Use This Calculator
- Select the length unit used for real measurements.
- Choose the focal source matching your calibration data.
- Enter fx and fy from the OpenCV camera matrix.
- Or enter lens and sensor data for conversion.
- Measure object width or height in pixels.
- Add real marker size from a ruler or datasheet.
- Use distortion coefficients only when points are not undistorted.
- Press calculate and read the result above the form.
Example Data Table
| Scenario | Real Size | Pixel Size | Focal Pixels | Expected Distance |
|---|---|---|---|---|
| Checkerboard square group | 12 cm | 180 px | 850 px | 56.67 cm |
| ArUco marker | 10 cm | 240 px | 840 px | 35 cm |
| Robot target plate | 8 cm | 120 px | 850 px | 56.67 cm |
| solvePnP vector | Not needed | Not needed | Camera matrix | √tx²+ty²+tz² |
Camera Calibration Distance Guide
Why camera calibration matters
Camera distance measurement looks simple. It is not always simple in practice. A camera does not measure depth directly. It records a projection of the world. Calibration connects that projection to physical scale. The camera matrix stores focal length in pixels. It also stores the principal point. These values let a pixel measurement become a distance estimate.
In physics, this is a pinhole model problem. A larger apparent object means a shorter distance. A smaller apparent object means a longer distance. The relation stays useful when the object is planar. It also works best when the object faces the camera. Strong tilt changes the visible width. Then pose estimation gives better results.
Known size method
The common method uses a known marker width. Measure the real marker width first. Then measure the marker width in the image. Use the calibrated focal length. The formula gives depth from similar triangles. It is fast and practical. It suits rulers, checkerboards, labels, and ArUco markers.
The same idea works with height. This calculator can average width and height results. Averaging can reduce small measurement errors. It can also reveal bad data. If width and height distances differ greatly, check marker tilt. Check focus and blur too. Pixel selection often dominates the error.
Sensor based focal conversion
Some users know the lens focal length in millimeters. That value is not enough alone. Pixel calculations need focal length in pixels. Sensor width and image width convert it. The conversion assumes the stated sensor crop is correct. Digital zoom changes the effective value. Resized images also change focal pixels.
For careful work, calibrate with checkerboard images. Save fx, fy, cx, cy, and distortion coefficients. OpenCV calibration returns these values. The calculator accepts them directly. It also estimates field of view. Field of view helps validate your camera setup.
Distortion and uncertainty
Lens distortion bends straight rays. Wide lenses show this strongly. Undistort points before measuring pixels. This calculator includes a radial correction option. It is an approximation for quick checks. For research, use undistorted image points from your vision pipeline.
Uncertainty matters in real experiments. Marker size error, pixel error, and focal error combine. The calculator reports an estimated range. This range is not a guarantee. It is a guide for repeatability. Take several images. Use the median distance. Keep lighting stable. Keep the marker sharp. Avoid motion blur and shadows.
Pose vector method
When you run solvePnP, OpenCV returns a translation vector. Its components describe target position in camera coordinates. The Euclidean norm gives total distance from the camera origin. The z component gives forward depth. Both are useful. This calculator supports the vector norm for advanced workflows.
Use consistent units everywhere. If object dimensions are centimeters, distances are centimeters. If pose values are meters, select meters. Mixing units breaks the result. Review inputs before trusting automated distance estimates in production.
Frequently Asked Questions
What does this calculator measure?
It estimates distance from a calibrated camera to a known object. It uses focal length, pixel size, marker size, or translation vector data.
Which focal length should I enter?
Enter fx and fy from the camera matrix. These values are in pixels. They are better than lens millimeter values for image measurements.
Can I use lens focal length in millimeters?
Yes. Select the sensor method. Then enter focal length, sensor size, and image size. The calculator converts millimeters to pixels.
What is the known size method?
It compares real object size with its pixel size. Similar triangles then give distance using the calibrated focal length.
Why are width and height distances different?
The object may be tilted, blurred, distorted, or measured poorly. Perspective changes apparent size when the surface is not frontal.
Should I undistort the image first?
Yes, for best accuracy. Undistorted points reduce lens curvature effects. The included radial option is only a quick approximation.
What does solvePnP distance mean?
solvePnP estimates target pose. The translation vector norm gives straight distance from camera origin to target coordinate origin.
Does z distance equal total distance?
No. z is forward depth. Total distance also includes x and y offsets. Use vector norm for true straight distance.
What unit should I select?
Select the same unit used for real object dimensions. The output follows that unit and also shows meter conversion.
How can I reduce error?
Use sharp images, correct calibration, undistorted points, and a flat marker. Measure pixels at high resolution when possible.
Can this work for moving objects?
Yes, if blur is controlled and object size is known. Fast motion needs short exposure and reliable detection.