Depth from Stereo Calculator

An engineering tool to calculate the depth of an object using two cameras based on the principles of stereo vision.

Disparity must be a positive number. Ensure x1 > x2 for a valid calculation.

What is Calculating Depth Using 2 Cameras?

Calculating depth using two cameras, a technique known as **stereo vision** or stereopsis, is the process of inferring the three-dimensional distance to objects from two-dimensional images. Much like human vision, it relies on capturing a scene from two slightly different viewpoints simultaneously. The difference in the object’s apparent position in the two images, called **disparity**, is the key to calculating its distance. The further away an object is, the smaller its disparity, and vice-versa.

This method is fundamental in fields like robotics, autonomous vehicles, 3D mapping, and augmented reality. For example, a self-driving car might use stereo cameras to judge the distance to pedestrians and other vehicles. A common misunderstanding is that camera resolution is the most critical factor; however, the accuracy of a stereo system is more dependent on the **baseline** (the distance between the cameras) and the precision of the disparity measurement. To reliably **calculate depth using 2 cameras**, the system must be carefully calibrated.

The Formula to Calculate Depth Using 2 Cameras

The core of stereo vision is the triangulation formula. For a simplified parallel camera setup (where both cameras are aligned and facing the same direction), the depth (Z) can be calculated using the following formula:

Z = (B × f) / d

This equation shows that depth is directly proportional to the baseline and focal length, and inversely proportional to the disparity. A larger baseline or focal length will result in better depth resolution for distant objects.

Variables Table

The variables required to calculate depth using 2 cameras.

Variable	Meaning	Unit	Typical Range
Z	Depth	mm, cm, m, in	Application-dependent (cm to km)
B	Baseline	mm, cm, m, in	60mm (human-like) to several meters (aerial)
f	Focal Length	mm, cm, in (or pixels)	4mm (wide-angle) to 50mm+ (standard)
d	Disparity (x₁ – x₂)	Pixels (px)	1 to several hundred pixels

Practical Examples

Example 1: Robotics Application

A small robot uses a stereo camera to navigate a workshop and avoid obstacles. The system has the following parameters:

• Inputs:
  • Focal Length (f): 8 mm
  • Baseline (B): 120 mm (12 cm)
  • Object Position in Left Image (x₁): 950 px
  • Object Position in Right Image (x₂): 870 px
• Calculation:
  • Disparity (d) = 950 – 870 = 80 px
  • Depth (Z) = (120 mm × 8 mm) / 80 px = 12 mm. This is incorrect, as focal length units must be in pixels or disparity must be in mm. A proper calculation requires converting focal length to pixels. Assuming a pixel size, if f=1600 pixels, then Z = (120 * 1600) / 80 = 2400 mm or 2.4 meters.
• Result: The object is approximately 2.4 meters away from the robot.

Example 2: Aerial Surveying

A drone equipped with a high-resolution stereo rig is used to create a 3D map of a landscape.

• Inputs:
  • Focal Length (f): 25 mm (equivalent to 4000 pixels on its sensor)
  • Baseline (B): 1 meter (1000 mm)
  • A point on a distant hill appears at x₁ = 2105 px and x₂ = 2101 px.
• Calculation:
  • Disparity (d) = 2105 – 2101 = 4 px
  • Depth (Z) = (1000 mm × 4000 px) / 4 px = 1,000,000 mm
• Result: The hill is 1,000,000 mm or 1 kilometer away. This demonstrates how a wide baseline is crucial for measuring large distances.

How to Use This Depth from Stereo Calculator

1. Enter Focal Length (f): Input the focal length of your cameras. If you don’t know it, you can often find it in your camera’s specifications. For this calculator, focal length can be entered in length units (mm, cm, in) assuming a simplified model.
2. Enter Baseline (B): Measure and enter the exact distance between the centers of your two camera lenses. This is a critical measurement for accuracy.
3. Select Units: Choose the units (millimeters, centimeters, or inches) you used for the baseline and focal length. The final depth calculation will be presented in this same unit.
4. Enter Pixel Coordinates: Identify a distinct point on an object in both the left and right images. Record the horizontal (x-axis) pixel coordinate for the point from each image and enter them as x₁ (left) and x₂ (right).
5. Interpret the Results: The calculator instantly provides the calculated depth (Z). It also shows the intermediate disparity value, which is essential for understanding the relationship between pixel shift and distance.

Key Factors That Affect Depth Calculation

Several factors influence the accuracy and range when you want to calculate depth using 2 cameras:

• Baseline: A wider baseline increases depth accuracy, especially for distant objects, but can make it harder to find matching points (the correspondence problem). A narrow baseline is better for close-range work.
• Focal Length: A longer focal length provides a narrower field of view and magnifies the scene, which can increase the pixel disparity for a given depth, improving precision.
• Image Rectification: For the simple formula to work, the two images must be perfectly aligned as if taken from parallel cameras. This process, called stereo rectification, corrects for any rotational misalignment and simplifies the search for matching points to a single horizontal line.
• Camera Calibration: Precise knowledge of the cameras’ intrinsic (focal length, optical center) and extrinsic (relative position and orientation) parameters is vital for accurate depth maps.
• Correspondence Algorithm: The software method used to find matching points (e.g., Block Matching, Semi-Global Block Matching) in the two images is crucial. Textural variety in the scene is important; featureless surfaces like white walls are very difficult to match.
• Lighting and Synchronization: Both cameras must capture the images at the exact same moment. Any time lag, especially in dynamic scenes, will lead to incorrect disparity and depth values. Consistent lighting is also important for matching features.

Frequently Asked Questions (FAQ)

1. What happens if the disparity is zero or negative?

A disparity of zero implies the object is infinitely far away. A negative disparity (where x₂ > x₁) means the point is “behind” the cameras’ convergence plane or the images were swapped. This calculator requires a positive disparity.

2. How do I find my camera’s focal length?

Focal length is usually printed on the lens itself (e.g., “8mm”). For smartphone or integrated cameras, you can find it in the image’s EXIF metadata or the device’s technical specifications. It can also be determined through a process called camera calibration.

3. Why is a wider baseline better for far objects?

For a distant object, the difference in viewing angle between two closely spaced cameras is tiny, resulting in a very small, hard-to-measure disparity. Increasing the baseline exaggerates this difference, creating a larger, more measurable disparity and thus more reliable depth estimation.

4. What is a “disparity map”?

A disparity map is an image where each pixel’s intensity value represents the calculated disparity for that point in the scene. It provides a dense, per-pixel representation of depth, often visualized with closer objects appearing brighter than farther ones.

5. Do I need special cameras for this?

While any two cameras can theoretically be used, dedicated stereo cameras are designed with fixed baselines and synchronized shutters, which greatly simplifies the process and improves accuracy. Using two separate cameras requires a rigid mount and a method to trigger them simultaneously.

6. What is “image rectification”?

Rectification is a transformation process applied to both images to make them appear as if they were taken by two perfectly parallel and aligned cameras. This ensures that a point in one image lies on the same horizontal row (scanline) in the other, drastically simplifying the search for corresponding points.

7. Why can’t the calculator find the depth of a blank wall?

This is the “correspondence problem.” To calculate disparity, the algorithm needs to find unique, matching features in both images. A blank, textureless surface has no distinct features to match, so the algorithm fails to find a correspondence and cannot calculate depth.

8. How does the unit selection work?

The unit selector ensures consistency. The formula Z = (B * f) / d works correctly only when B and the output Z are in the same units, and f and d are also in consistent units (e.g., pixels). This calculator simplifies this by assuming your input units for B and f will be the same as your output unit for Z.