Astrophotography Image Scale Calculator
Created by: Ethan Brooks
Last updated:
Calculate arcseconds per output pixel from physical pixel pitch, effective focal length and square binning, with explicit small-angle assumptions.
Astrophotography Image Scale Calculator
Astronomy & AstrophotographySky angle per output pixel
What is astrophotography image scale?
An astrophotography image scale calculator estimates how much sky angle corresponds to one output pixel. Enter the camera's physical pixel pitch, the effective focal length of the imaging system and an integer square binning factor. The result is expressed in arcseconds per pixel. It describes the spacing of samples in an image near the optical axis, rather than the total frame width, telescope magnification or the smallest detail that an observation will reveal.
Pixel pitch is the physical distance between neighboring sensor samples, usually specified in micrometers. It is not the camera's megapixel count, the width of the complete sensor or the dimensions of an exported photograph. This calculator assumes square pixels. Focal length means the effective optical focal length at the camera, including any reducer or amplifier already in use. Enter that complete value once; the form does not apply an additional accessory multiplier or infer one from mechanical spacing.
Binning changes the output sampling interval when neighboring pixels are grouped into larger samples. Here, an integer n means square n by n grouping, so a factor of two spans two native pixel pitches along each axis. Enter one for an unbinned image. The geometric result does not establish whether a camera performs charge combination before readout or digital combination afterward, and it does not calculate a noise reduction or a change in sensor sensitivity.
The starting values are illustrative and should be replaced with specifications for your setup. A smaller angular interval does not automatically mean a better image. Focus, tracking, atmospheric conditions, optics and processing still affect recorded detail. Keep the result with its inputs when copying it into an observing log or another application. The model is a local small-angle approximation, not a distortion map or a measurement obtained by identifying stars in an actual exposure.
How the calculation works
Convert the native pixel pitch from micrometers to millimeters, multiply by the square binning factor and divide by effective focal length in millimeters. This gives the local angular interval in radians under the small-angle approximation. Multiplying by 648000 divided by π converts radians to arcseconds. With pitch entered in micrometers, the combined coefficient is 648 divided by π, approximately 206.264806. Diffraction Limited documents the pitch-to-focal-length relationship using a rounded coefficient of 206.
The implementation retains π and rounds only the displayed results. It accepts positive finite lengths and a positive safe integer binning factor. To keep the approximation's domain explicit, output pitch divided by focal length must be no greater than 0.001 in matching units. This is a conservative implementation guard, not a manufacturer limit. Square grouping is a geometric assumption: the result does not certify supported camera modes. Edits clear the previous result, and changing focal-length units converts the existing measurement while preserving blank fields.
Formula and symbols
s = (648 / π) × p × n / F arcsec/pixel; output pitch = p × n. Domain: (p × n / 1000) / F ≤ 0.001.
- p: Native physical pixel pitch (µm)
- n: Square binning factor (integer)
- F: Effective focal length (mm)
How to use the calculator
- Enter effective focal length. Choose millimeters or inches and enter the focal length at the camera, including optical accessory effects once.
- Enter native pixel pitch. Use the camera's physical pixel pitch in micrometers, before binning.
- Specify square binning. Enter a positive integer n for n × n grouping; one means unbinned.
- Calculate and review scope. Read arcseconds per output pixel with the small-angle assumptions. The result does not grade image quality or noise.
Worked examples
Calculate an illustrative imaging setup
For native pitch 3.76 µm, effective focal length 800 mm and binning one, the result is approximately 0.969 arcseconds per output pixel. Record all three inputs with the scale so that another person can reproduce it. The number describes the local sampling interval. It does not include seeing, guiding error or a claim that two objects separated by that angle will be resolved in the resulting image.
Account for square grouping
Keeping the same 3.76 µm native pitch and 800 mm effective focal length, enter two for square binning. The output pitch becomes 7.52 µm and the scale becomes approximately 1.939 arcseconds per output pixel. Four native samples form a two-by-two group, but the linear scale doubles rather than quadruples. This example describes geometry only; charge binning and software combination need not have identical noise behavior or camera support.
Check a published reference
Diffraction Limited gives a rounded example of a 9 µm pixel with a 2000 mm focal length producing 0.93 arcseconds. Enter those values with binning one to obtain approximately 0.928 arcseconds per pixel, consistent with that rounded reference. The calculator uses the radian conversion rather than the article's shortened coefficient. Its result retains the units and assumptions without adopting the article's broader recommendations about particular cameras or observing conditions.
Practical applications
- Record an imaging configuration. Store physical pitch, effective focal length and binning beside the angular scale so that a later change in camera settings does not leave an unexplained number associated with the wrong exposure or equipment arrangement.
- Check an input requested by imaging software. Confirm whether that program expects native sensor pitch, output pitch or arcseconds per output pixel before copying a value. Those quantities are related, but they have different units and should not be substituted without checking the field's meaning.
- Audit a binning entry in a worksheet. A two-by-two group contains four pixels, yet spans only two native pitches per axis. Keeping the linear factor explicit helps identify an accidental factor-of-four change in an image-scale calculation or an equipment note.
- Record the effect of an optical configuration change. Supply the effective focal length of the actual arrangement and calculate its sampling interval. Establish the applicable focal length separately; this tool cannot verify accessory spacing, focus travel or a nominal reducer factor.
- Prepare a reference for subsequent analysis. Image scale can accompany separately measured star widths or other angular measurements. This calculator does not turn those measurements into a universal camera suitability score or prescribe a preferred sampling band for every imaging task.
- Explain angular units in a teaching example. One degree contains sixty arcminutes and each arcminute contains sixty arcseconds. The reported scale associates that angular unit with one output sample, keeping a pixel interval distinct from a complete sensor field or an optical resolution criterion.
Tips for reliable inputs
Use the native physical pitch from the camera specification and apply binning once. If you enter an already binned effective pitch, leave the grouping factor at one and note that convention. Avoid substituting a display pixel size or an image's dimensions in pixels for the sensor's physical pitch. Check that the focal length belongs to the complete imaging configuration.
Cropping an image without resampling retains its pixel spacing while changing its coverage. Resizing, interpolation or drizzle can change the output grid and need a separate account of that transformation. Do not apply this result unchanged to an arbitrarily resized export. For a real image with uncertain metadata, use an appropriate astrometric calibration rather than treating this nominal geometry as a measurement.
Frequently asked questions
What is image scale in astrophotography?
Image scale describes the angular interval associated with an image pixel, commonly in arcseconds per pixel. This calculator estimates it from physical pixel pitch, effective focal length and square binning. It is a sampling interval near the optical axis, not the total field of view or a promise about resolved detail. Keep the inputs and assumptions with the number.
Which focal length should I enter?
Enter the effective focal length at the camera for the complete optical configuration. If a documented reducer or amplifier changes the telescope's focal length, account for that change before entering the value. Do not apply the same factor twice. The calculator converts millimeters and inches but does not determine accessory spacing, optical compatibility or an unknown effective focal length.
Does two-by-two binning multiply scale by four?
No. Two-by-two grouping contains four native pixels but spans two pixel pitches along each axis, so the linear angular scale doubles. The calculator's binning field expects that linear factor: enter two for two-by-two grouping. This describes the output sampling geometry only. It does not predict camera read noise, sensitivity, frame rate or whether the selected mode is supported.
Is hardware binning equivalent to software binning?
They can describe the same output spacing when they combine matching groups of pixels, but the readout and noise behavior can differ. Charge combination before readout is distinct from combining digitized samples afterward. This calculator only applies the geometric grouping factor. Check the camera and software documentation for the actual mode, especially when interpreting color data or noise performance.
Does a smaller number always produce better images?
No. A smaller scale means a finer angular sampling interval, but it does not by itself establish improved detail or a better camera match. Optical quality, atmosphere, focus, tracking and processing also matter. The calculator does not assume a seeing value or grade sampling quality. Use the result as one documented property of the imaging setup, alongside separate measurements.
Can I use this for resized or cropped images?
A crop that retains the original pixel grid preserves the local scale while reducing coverage. Resampling changes the grid, so the resulting output spacing needs its own transformation. This form models native pitch with integer square grouping and does not model arbitrary resizing, interpolation, drizzle or distortion. Keep the processing history with any scale assigned to a finished image.
Sources and method limits
- Diffraction Limited: CMOS technology and pixel size — Doug George; publication date not displayed in inspected article; Conventional Wisdom, image-scale formula and 9 µm / 2000 mm example. Accessed 2026-10-07. Angular pixel scale proportional to pixel pitch / focal length; rounded example 0.93 arcsec. Implementation derives 206.264806… from radians and unit conversion rather than using the article's rounded 206. Sampling recommendations and noise claims are not encoded.
- Teledyne Vision Solutions: Binning — Imaging Fundamentals; publication date not displayed; Introduction, CCD/EMCCD Binning and CMOS Binning. Accessed 2026-10-07. Square n × n grouping increases linear output-pixel pitch by n. Physical charge binning and digital combination have different readout behavior; no SNR, speed or universal hardware-support claim is calculated.
- NIST: Guide to the SI, Appendix B.9 — conversion factors — SP 811 online appendix; Length and Angle conversion tables. Accessed 2026-10-07. Length conversions: 1 in = 25.4 mm and 1 international mile = 1.609344 km. Degrees, arcminutes and arcseconds are angle units; calculations retain π rather than rounded tabular radian factors.
Examples are illustrative calculations, not equipment endorsements. Use each method within its stated geometry and optical assumptions.