Pixel Size Calculation: Determine Sensor & Angular Resolution

Accurately calculate the physical pixel size (pixel pitch) and angular pixel size (angular resolution) of your camera sensor or imaging system based on matrix dimensions and field of view. This tool is essential for photographers, astronomers, and engineers.

Pixel Size Calculator

What is Pixel Size Calculation?

Pixel size calculation is a fundamental process in imaging science, photography, and machine vision that determines the dimensions of individual pixels on an image sensor, both physically and angularly. Understanding pixel size is crucial for evaluating image quality, system resolution, and overall performance of a camera or optical system. This calculation helps professionals and enthusiasts alike to make informed decisions about equipment and imaging strategies.

Definition of Pixel Size

When we talk about pixel size calculation, we typically refer to two distinct but related concepts:

• Physical Pixel Size (Pixel Pitch): This is the actual physical dimension of a single photosensitive element (pixel) on the image sensor, usually measured in micrometers (µm). It’s calculated by dividing the sensor’s physical dimension (width or height) by the number of pixels along that dimension. A smaller pixel pitch generally means more pixels can fit on a given sensor area, leading to higher resolution, but can also impact low-light performance.
• Angular Pixel Size (Angular Resolution): This refers to the angular extent that each pixel covers in the scene being imaged, typically measured in degrees per pixel, milliradians per pixel (mrad/pixel), or arcseconds per pixel. It’s calculated by dividing the Field of View (FOV) by the number of pixels across that FOV. A smaller angular pixel size indicates that each pixel captures a finer detail of the scene, leading to higher angular resolution.

Who Should Use This Pixel Size Calculation Tool?

This pixel size calculation tool is invaluable for a wide range of users:

• Photographers: To understand how sensor size, pixel count, and lens choice affect the detail captured in their images, especially for specialized fields like astrophotography or macro photography.
• Astronomers: For planning observations, matching telescopes to cameras, and determining the resolution of celestial objects captured.
• Machine Vision Engineers: To design systems that meet specific resolution requirements for inspection, measurement, or quality control.
• Drone Operators & Surveyors: To plan flight paths and camera settings for aerial mapping and photogrammetry, ensuring sufficient ground sampling distance (GSD).
• Optical System Designers: To optimize sensor and lens combinations for desired performance characteristics.

Common Misconceptions about Pixel Size Calculation

Several misunderstandings often arise regarding pixel size calculation:

• “More pixels always means better image quality”: While higher pixel counts can lead to higher resolution, smaller pixels can sometimes suffer from increased noise in low light or be limited by diffraction, negating the resolution advantage.
• “Pixel size is only about physical dimensions”: Neglecting angular pixel size means overlooking how much detail each pixel captures from the scene, which is critical for system performance.
• “Focal length alone determines resolution”: Focal length influences FOV, which in turn affects angular pixel size, but the actual pixel count and sensor dimensions are equally important for the final pixel size calculation.

Pixel Size Calculation Formula and Mathematical Explanation

Understanding the underlying formulas for pixel size calculation is key to appreciating the results. Our calculator uses straightforward geometric principles to determine both physical and angular pixel sizes.

Step-by-Step Derivation

The pixel size calculation involves two main components:

1. Physical Pixel Size (Pixel Pitch)

This calculation determines the actual dimension of a single pixel on the sensor. It’s a direct ratio of the sensor’s physical dimension to the number of pixels along that dimension.

• Horizontal Physical Pixel Size (µm):
  (Sensor Width (mm) / Matrix Width (pixels)) * 1000
  (Multiplying by 1000 converts millimeters to micrometers)
• Vertical Physical Pixel Size (µm):
  (Sensor Height (mm) / Matrix Height (pixels)) * 1000

2. Angular Pixel Size (Angular Resolution)

This calculation determines the angular extent covered by a single pixel in the scene. It’s a direct ratio of the Field of View (FOV) to the number of pixels across that FOV.

• Horizontal Angular Pixel Size (degrees/pixel):
  Horizontal FOV (degrees) / Matrix Width (pixels)
• Derivation of Vertical FOV: To maintain consistency and simplify inputs, the vertical FOV is derived from the horizontal FOV and the matrix aspect ratio. This assumes the sensor’s aspect ratio matches the matrix’s aspect ratio, which is common.
  Matrix Aspect Ratio = Matrix Width (pixels) / Matrix Height (pixels)
Vertical FOV (degrees) = Horizontal FOV (degrees) / Matrix Aspect Ratio
• Vertical Angular Pixel Size (degrees/pixel):
  Vertical FOV (degrees) / Matrix Height (pixels)

For more practical units, angular pixel size is often converted to milliradians (mrad) or arcseconds (arcsec):

• 1 degree = 17.4533 milliradians
• 1 degree = 3600 arcseconds

Variable Explanations and Table

Here’s a breakdown of the variables used in the pixel size calculation:

Table 1: Variables for Pixel Size Calculation

Variable	Meaning	Unit	Typical Range
Sensor Width	Physical width of the image sensor	mm	5 – 40 mm
Sensor Height	Physical height of the image sensor	mm	3 – 30 mm
Matrix Width	Number of pixels horizontally	pixels	1000 – 10000 pixels
Matrix Height	Number of pixels vertically	pixels	800 – 7000 pixels
Horizontal FOV	Horizontal angular extent of the scene	degrees	10 – 120 degrees
Horizontal Physical Pixel Size	Physical width of one pixel on the sensor	µm	1 – 10 µm
Horizontal Angular Pixel Size	Angular extent covered by one pixel horizontally	mrad/pixel, arcsec/pixel	0.01 – 1 mrad/pixel

Practical Examples (Real-World Use Cases)

Let’s explore how pixel size calculation applies to real-world scenarios, demonstrating the utility of this tool.

Example 1: Astrophotography Setup

An astrophotographer wants to capture fine details of a nebula. They are using a camera with an APS-C sensor and a telescope that provides a specific field of view.

• Inputs:
  • Sensor Width: 23.5 mm
  • Sensor Height: 15.6 mm
  • Matrix Width: 6000 pixels
  • Matrix Height: 4000 pixels
  • Horizontal Field of View: 1.5 degrees (narrow FOV typical for telescopes)
• Pixel Size Calculation Output:
  • Horizontal Physical Pixel Size (Pitch): (23.5 / 6000) * 1000 = 3.92 µm
  • Vertical Physical Pixel Size (Pitch): (15.6 / 4000) * 1000 = 3.90 µm
  • Horizontal Angular Pixel Size: (1.5 / 6000) degrees/pixel = 0.00025 degrees/pixel ≈ 0.00436 mrad/pixel ≈ 0.9 arcsec/pixel
  • Vertical Angular Pixel Size: (Derived Vertical FOV: 1.5 / (6000/4000) = 1 degree) / 4000 pixels = 0.00025 degrees/pixel ≈ 0.00436 mrad/pixel ≈ 0.9 arcsec/pixel
  • Total Pixels: 24,000,000 (24 MP)
• Interpretation: The small angular pixel size (0.9 arcsec/pixel) indicates that this setup can resolve very fine details in the night sky, which is crucial for astrophotography. The physical pixel size of ~3.9 µm is a good balance for sensitivity and resolution on an APS-C sensor.

Example 2: Industrial Inspection Camera

A manufacturing company needs a camera system to inspect small defects on circuit boards. They need to ensure a certain level of detail can be resolved across a specific area.

• Inputs:
  • Sensor Width: 8.8 mm (1-inch type sensor)
  • Sensor Height: 6.6 mm
  • Matrix Width: 4000 pixels
  • Matrix Height: 3000 pixels
  • Horizontal Field of View: 10 degrees (to cover a specific inspection area)
• Pixel Size Calculation Output:
  • Horizontal Physical Pixel Size (Pitch): (8.8 / 4000) * 1000 = 2.2 µm
  • Vertical Physical Pixel Size (Pitch): (6.6 / 3000) * 1000 = 2.2 µm
  • Horizontal Angular Pixel Size: (10 / 4000) degrees/pixel = 0.0025 degrees/pixel ≈ 0.0436 mrad/pixel ≈ 9 arcsec/pixel
  • Vertical Angular Pixel Size: (Derived Vertical FOV: 10 / (4000/3000) = 7.5 degrees) / 3000 pixels = 0.0025 degrees/pixel ≈ 0.0436 mrad/pixel ≈ 9 arcsec/pixel
  • Total Pixels: 12,000,000 (12 MP)
• Interpretation: The very small physical pixel size (2.2 µm) allows for high pixel density, which is excellent for resolving minute defects. The angular pixel size of 9 arcsec/pixel means that within the 10-degree FOV, very small angular features can be distinguished, making it suitable for detailed inspection. This pixel size calculation confirms the system’s capability.

How to Use This Pixel Size Calculation Calculator

Our intuitive pixel size calculation tool is designed for ease of use. Follow these steps to get your results:

Step-by-Step Instructions

1. Enter Sensor Width (mm): Input the physical width of your camera’s image sensor in millimeters. This is often found in your camera’s specifications or sensor datasheets.
2. Enter Sensor Height (mm): Input the physical height of your camera’s image sensor in millimeters.
3. Enter Matrix Width (pixels): Input the total number of pixels horizontally across your sensor. This is the horizontal resolution of your image.
4. Enter Matrix Height (pixels): Input the total number of pixels vertically down your sensor. This is the vertical resolution of your image.
5. Enter Horizontal Field of View (degrees): Input the horizontal angular extent that your lens and sensor combination captures, in degrees. This can often be found in lens specifications or calculated using focal length and sensor size (though for this calculator, it’s a direct input).
6. Click “Calculate Pixel Size”: Once all fields are filled, click this button to perform the pixel size calculation. The results will appear below.
7. Click “Reset”: To clear all inputs and return to default values, click the “Reset” button.

How to Read the Results

The results section provides several key metrics from the pixel size calculation:

• Horizontal Angular Pixel Size (Primary Result): This is the most prominent result, showing the angular resolution per pixel horizontally. A smaller value indicates finer detail capture. It’s displayed in degrees/pixel, mrad/pixel, and arcsec/pixel.
• Vertical Angular Pixel Size: Similar to the horizontal, but for the vertical dimension.
• Horizontal Physical Pixel Size (Pitch): The actual physical width of a single pixel on your sensor in micrometers (µm).
• Vertical Physical Pixel Size (Pitch): The actual physical height of a single pixel on your sensor in micrometers (µm).
• Total Pixels: The total number of pixels on your sensor (Matrix Width × Matrix Height).

Decision-Making Guidance

Use the results of your pixel size calculation to guide your decisions:

• For high detail: Aim for smaller angular pixel sizes. This might mean using a longer focal length lens (to narrow FOV) or a sensor with more pixels.
• For low-light performance: Larger physical pixel sizes (pixel pitch) generally gather more light, leading to better low-light performance, but at the cost of fewer pixels for a given sensor size.
• Matching components: Ensure your lens’s resolving power (often measured in line pairs per millimeter) is sufficient to take advantage of your sensor’s physical pixel size.
• System design: For machine vision or surveillance, the angular pixel size directly relates to the smallest feature you can reliably detect at a given distance.

Key Factors That Affect Pixel Size Calculation Results

Several critical factors influence the outcome of a pixel size calculation and, consequently, the performance of an imaging system. Understanding these helps in optimizing your setup.

1. Sensor Dimensions (Physical Size): The actual width and height of the image sensor directly determine the physical pixel size when combined with the matrix dimensions. A larger sensor allows for larger pixels at the same resolution, or more pixels at the same pixel size.
2. Matrix Dimensions (Pixel Count): The number of horizontal and vertical pixels on the sensor is a primary input for both physical and angular pixel size calculation. More pixels on the same sensor size mean smaller physical pixels and finer angular resolution for a given FOV.
3. Field of View (FOV): The angular extent of the scene captured by the lens and sensor is crucial for angular pixel size calculation. A narrower FOV (e.g., with a telephoto lens) will result in a smaller angular pixel size, meaning each pixel covers a smaller portion of the scene and thus captures more detail.
4. Focal Length of the Lens: While not a direct input in this specific calculator (as FOV is provided), focal length is the primary determinant of the Field of View for a given sensor size. A longer focal length reduces the FOV, leading to a smaller angular pixel size and higher magnification.
5. Optical System Quality (Diffraction Limit): The quality of the lens and the aperture setting can limit the effective resolution, regardless of how small your pixels are. Diffraction, an optical phenomenon, sets a fundamental limit on how small a point of light can be focused, which can effectively make very small pixels redundant if the lens cannot resolve that level of detail. This is a critical consideration beyond simple pixel size calculation.
6. Aspect Ratio: The ratio of sensor width to height, and matrix width to height, influences how horizontal and vertical pixel sizes relate. Our calculator derives vertical FOV based on the matrix aspect ratio for consistent pixel size calculation.
7. Distance to Subject: Although not part of the intrinsic pixel size calculation, the distance to the subject, combined with angular pixel size, determines the Ground Sampling Distance (GSD) or the real-world size of the smallest feature a single pixel can resolve. This is vital for applications like aerial mapping.

Frequently Asked Questions (FAQ) about Pixel Size Calculation

What is the main difference between physical pixel size (pixel pitch) and angular pixel size?

Physical pixel size (pixel pitch) refers to the actual dimensions of a pixel on the sensor surface, measured in micrometers (µm). Angular pixel size, or angular resolution, describes the angular extent that each pixel covers in the scene, measured in units like degrees/pixel or arcseconds/pixel. The former is about the sensor itself, the latter about what the sensor “sees” through the lens.

Why is pixel size calculation important for image quality?

Pixel size calculation is crucial because it directly impacts the detail an imaging system can capture. A smaller angular pixel size means finer details can be resolved. Physical pixel size affects light gathering capability and noise performance, especially in low light. Understanding both helps optimize for resolution, sensitivity, and overall image fidelity.

Does a larger physical pixel size always mean better low-light performance?

Generally, yes. Larger physical pixels have a larger surface area to collect photons, leading to a higher signal-to-noise ratio and better performance in low-light conditions. However, this often comes at the cost of lower total pixel count for a given sensor size, reducing overall resolution.

How does focal length relate to pixel size calculation?

Focal length is a key determinant of the Field of View (FOV). A longer focal length results in a narrower FOV, which, for a given matrix width, leads to a smaller angular pixel size. This means a longer lens “magnifies” the scene, allowing each pixel to cover a smaller, more detailed portion of the subject. Our calculator uses FOV as a direct input, which is influenced by focal length.

Can I perform pixel size calculation without knowing the sensor dimensions?

You can calculate angular pixel size if you know the Field of View and the matrix dimensions (pixel count). However, to calculate the physical pixel size (pixel pitch), you absolutely need the sensor’s physical dimensions (width and height) in addition to the matrix dimensions.

What are typical pixel sizes (pixel pitch) for modern cameras?

Typical physical pixel sizes range from around 1 µm for small smartphone sensors to 6-8 µm or more for professional full-frame cameras and specialized scientific sensors. The trend for consumer cameras has been towards smaller pixels to pack more megapixels onto smaller sensors.

How does the diffraction limit affect pixel size calculation?

The diffraction limit is an optical phenomenon that dictates the smallest point of light a lens can focus. If your physical pixel size is significantly smaller than the diffraction-limited spot size of your lens at a given aperture, those extra pixels won’t capture additional detail; they’ll just record the same blurred spot over multiple pixels. This means the effective resolution might be limited by the lens, not the sensor’s pixel count.

What units are commonly used for angular pixel size?

Angular pixel size is commonly expressed in degrees per pixel, milliradians per pixel (mrad/pixel), or arcseconds per pixel. Arcseconds are particularly common in astronomy due to the very small angles involved when observing celestial objects.

Related Tools and Internal Resources

To further enhance your understanding of imaging systems and related calculations, explore our other specialized tools and articles:

• Camera FOV Calculator: Determine your camera’s field of view based on sensor size and focal length. Essential for planning your shots.
• Lens Focal Length Calculator: Calculate the effective focal length or determine the required focal length for a specific field of view.
• Sensor Size Calculator: Compare different sensor formats and their impact on image characteristics.
• Depth of Field Calculator: Understand how aperture, focal length, and distance affect the sharp area in your images.
• Resolution Calculator: Evaluate the overall resolution of your imaging system, considering both sensor and lens limitations.
• Image Quality Metrics Explained: A comprehensive guide to various metrics used to assess and compare image quality.