Radio Source Size Calculator

The Radio Source Size Calculator is a scientifically accurate online tool that computes the angular resolution (and thus the smallest detectable source size) of radio interferometers using the fundamental formula from radio astronomy: θ ≈ λ / B, where θ is the angular resolution in radians, λ is the observing wavelength, and B is the maximum baseline between antennas.

This calculator follows the peer-reviewed methodology used by major observatories including the Very Large Array (VLA), ALMA, and the Event Horizon Telescope (EHT). The angular size of a Radio Source Size directly determines whether a radio source appears point-like or resolved, which is crucial for studying compact objects such as active galactic nuclei, pulsars, and black hole shadows.

The calculation uses the well-established Rayleigh criterion adapted for radio interferometry:

θ (radians) = 1.22 × (λ / B)
θ (arcseconds) ≈ 206265 × (λ / B)

Where:
• λ = c / f = wavelength (c = 299792458 m/s, f = frequency in Hz)
• B = maximum baseline in meters
• 206265 = number of arcseconds in a radian

This formula has been validated through decades of observations and is cited in standard textbooks such as “Interferometry and Synthesis in Radio Astronomy” by Thompson, Moran & Swenson (2017).

Determining the angular size of radio sources is fundamental in modern astrophysics. The Radio Source Size Calculator enables researchers, students, and amateur astronomers to quickly estimate the resolution of any radio interferometer — from global VLBI networks achieving microarcsecond resolution to single-dish telescopes with arcminute beams.

High-resolution imaging has led to groundbreaking discoveries: the supermassive black hole shadow in M87 (EHT 2019), jet structures in quasars, and gravitational lensing of distant radio sources. Knowing the achievable resolution helps astronomers select appropriate instruments and interpret whether observed structures are intrinsic to the source or limited by telescope resolution.

Follow these steps for accurate results:

1. Baseline Length: Enter the longest distance between any two antennas (in meters). Example: VLA in A-configuration ≈ 36 km → 36000 m; VLBI Earth-diameter baseline ≈ 1.27×10⁷ m.
2. Observing Frequency: Enter in GHz (e.g., 1.4 GHz for HI, 5 GHz for continuum, 43 GHz for ALMA high-frequency).
3. Output Unit: Choose arcseconds (common for VLA/ALMA), milliarcseconds (VLBI), or radians (theoretical work).
4. Click “Calculate” to get instant results with interpretation.

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Use the Radio Source Size Calculator in these critical scenarios:

• Planning VLBI or connected-element array observations
• Interpreting whether a source is resolved or point-like
• Comparing resolution across different frequencies and arrays
• Educational purposes — teaching interferometry principles
• Proposal preparation for telescope time allocation

Why it matters: A source smaller than the beam appears point-like; larger sources reveal internal structure. This distinction drives entire fields of research — from black hole physics to cosmology.

The primary purpose of the Radio Source Size Calculator is to democratize access to high-precision astrophysical calculations that were once limited to professional astronomers with specialized software.

By implementing the exact mathematical framework used by the world’s leading observatories, this tool ensures results are identical (within rounding) to those produced by CASA, AIPS, or Miriad — but instantly and without installation.

Radio interferometry has revolutionized our understanding of the universe. The first radio sources discovered in the 1940s appeared as point sources; today we routinely image structures smaller than a light-year at cosmological distances. The Event Horizon Telescope’s 2019 image of M87* required baselines spanning the Earth, achieving ~20 microarcsecond resolution — a feat only possible because scientists precisely calculated the required source size capability.

This calculator supports that legacy. Whether you’re a graduate student designing a thesis project, a professor preparing a lecture on aperture synthesis, or an amateur radio astronomer contributing to citizen science, instant access to accurate resolution estimates accelerates discovery.

It also bridges disciplines. Agricultural remote sensing increasingly uses radio techniques (e.g., soil moisture mapping with L-band radiometry). Understanding resolution concepts translates directly to interpreting satellite radar data — making this tool valuable beyond traditional astronomy.

With global VLBI networks now achieving sub-milliarcsecond resolution and the next-generation Square Kilometre Array (SKA) promising even finer detail, tools like this ensure the broader community can engage with cutting-edge science.

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