Formula Used
This tool uses standard small-angle imaging geometry. The plate scale at the focal plane is:
Plate scale (arcsec/mm) = 206.264806 / f(mm)
For a camera sensor, the image scale per pixel is:
Scale (arcsec/pixel) = 206.264806 × pixel(µm) / f(mm)
Field of view uses the exact angle:
FOV = 2 × atan(size / (2f)) (converted to degrees)
How to Use This Calculator
- Enter your focal length and any reducer/Barlow factor.
- Add pixel size and binning to compute arcsec per pixel.
- Optionally enter sensor width and height for field of view.
- Optionally enter seeing to evaluate sampling quality.
- Press Calculate. Results appear above the form.
Example Data Table
| Setup | Focal (mm) | Pixel (µm) | Binning | Scale (″/px) | Sensor (mm) | FOV (°) |
|---|---|---|---|---|---|---|
| 80mm refractor, 480mm | 480 | 3.76 | 1×1 | 1.616 | 23.5 × 15.6 | 2.80 × 1.86 |
| Newtonian, 1000mm | 1000 | 2.90 | 1×1 | 0.598 | 17.7 × 13.4 | 1.01 × 0.77 |
| SCT with 0.63 reducer | 2032 × 0.63 | 3.76 | 2×2 | 1.204 | 13.2 × 8.8 | 0.75 × 0.50 |
Values are rounded and meant as reference examples.
Plate Scale Guide
1) What plate scale tells you
Plate scale links your optics to the sky by converting distance at the focal plane into angle. It answers, “How many arcseconds land on one millimeter?” Once you know that, you can translate camera pixels into arcseconds per pixel and predict how large objects will appear in your final image. It also helps you compare cameras quickly.
2) The 206.265 constant in practice
The calculator uses the small-angle relationship where one radian equals about 206,265 arcseconds. With focal length in millimeters, plate scale becomes 206.264806 / f arcsec per mm. For example, a 500 mm system gives ~0.4125″/mm, while a 2000 mm system gives ~0.1031″/mm.
3) Pixel size turns scale into sampling
To get arcseconds per pixel, multiply plate scale by pixel pitch (in mm). A 3.76 µm pixel is 0.00376 mm. At 800 mm focal length, the scale is ~0.970″/px. If you switch to 2.4 µm pixels at the same focal length, the scale tightens to ~0.619″/px.
4) Reducers, Barlows, and binning
Optical factors change effective focal length. A 0.8× reducer shortens focal length, increasing arcseconds per pixel and widening the field. A 2× Barlow doubles focal length, decreasing arcseconds per pixel for finer sampling. Binning increases effective pixel size; 2×2 binning roughly doubles arcseconds per pixel and improves signal per binned pixel.
5) Field of view from sensor dimensions
Field of view depends on both focal length and sensor size. This calculator uses the exact angle formula 2·atan(size/(2f)), then converts to degrees. As a quick reference, a 23.5 mm wide sensor at 480 mm produces ~2.80° width, while the same sensor at 1000 mm produces ~1.35°.
6) Sampling versus seeing
Seeing (often 1–4″ for many locations) sets a practical resolution limit. Many imagers aim for about 2–3 pixels across the seeing FWHM. If seeing is 2.5″, a target scale near 1.0″/px gives ~2.5 px/FWHM (balanced). Much smaller scales can oversample, increasing noise and guiding demands without adding real detail.
7) Matching scale to your targets
Wide nebulae and large galaxies often look best with 1–3″/px and a generous field. Small galaxies, planetary nebulae, and lunar/solar detail usually benefit from 0.2–0.8″/px if your atmosphere supports it. Use the field-of-view numbers to confirm framing, and use the sampling check to judge whether your scale fits typical conditions.
8) A practical setup checklist
Start by entering focal length and any reducer or Barlow. Add pixel size and binning to see arcseconds per pixel. Then enter sensor width and height to verify framing. Finally, enter a realistic seeing value to evaluate pixels per FWHM and adjust with binning, focal length, or camera choice until your scale and field match your imaging goals.
FAQs
1) What is a good arcseconds-per-pixel value?
For deep-sky imaging, many setups land between 0.7″/px and 2.5″/px. Your local seeing matters: aim for roughly 2–3 pixels across the seeing FWHM for balanced detail and noise.
2) Does a smaller arcseconds-per-pixel always mean sharper images?
No. If your scale is much smaller than what seeing allows, you oversample and gain little detail while increasing noise and tracking requirements. Matching scale to seeing usually improves real-world results.
3) Should I use the small-angle formula or the exact field-of-view formula?
For plate scale, the small-angle approach is standard and accurate for typical telescope fields. For field of view, the calculator uses the exact atan formula, which stays accurate even for wider sensors.
4) How do reducers and Barlows affect my numbers?
They change effective focal length. Reducers (e.g., 0.63×) increase scale and widen the field. Barlows (e.g., 2×) decrease scale and narrow the field, pushing you toward finer sampling.
5) What does binning do to plate scale?
Binning increases effective pixel size. With 2×2 binning, the effective pixel pitch doubles, so arcseconds per pixel roughly doubles too. This can help in poor seeing or when signal-to-noise is the priority.
6) I don’t know my sensor size. Can I still use this?
Yes. Enter focal length, factor, pixel size, and binning to get arcseconds per pixel. Sensor dimensions are only needed to compute field of view. You can add them later when framing a target.
7) Why does the calculator ask for seeing?
Seeing lets the tool estimate pixels per FWHM, which is a quick sampling check. It helps you decide whether you are undersampling, balanced, or oversampling for your typical night-sky conditions.