Flux Density & Apparent Magnitude Converter

Convert between flux density (Jy, mJy, μJy) and apparent magnitude in AB or Vega systems. Also converts flux ratios to magnitude differences for any UBVRIJHK filter.

💫 Flux Density & Apparent Magnitude Converter
Magnitude System
Filter Band
Apparent Magnitude (m)
mag
Flux Density
Magnitude Difference (Δm = m₂ − m₁)
mag
Or enter two flux densities (same units) to get Δm
Flux Density
—
Flux in W/m²/Hz (SI)
—
Flux in erg/s/cm²/Hz (CGS)
—
Zero-Point (F₀)
—
Filter Effective Wavelength
—
Input Magnitude
—

💫 What Are Flux Density and Apparent Magnitude?

Apparent magnitude is the traditional astronomical measure of how bright an object appears in the sky as seen from Earth. It is defined on a logarithmic scale: a difference of 5 magnitudes corresponds to a flux ratio of exactly 100. The formula is m = −2.5 log₁₀(F/F₀), where F is the measured flux density and F₀ is the zero-point flux density for the chosen magnitude system. The scale is inverted: brighter objects have smaller (more negative) magnitudes. The Sun has m = −26.74, Sirius is −1.46, and the faintest objects detectable by JWST are around m = +31.

Flux density (spectral flux density) is the power received per unit area per unit frequency interval, measured in Janskys (1 Jy = 10−26 W/m²/Hz). This is a physically meaningful, linear quantity unlike the logarithmic magnitude scale. It is essential for computing luminosities, comparing multi-wavelength observations, and calibrating detectors. Converting between magnitudes and flux densities requires knowing the magnitude system and filter used.

Two major magnitude systems are in use. The Vega system uses the star Vega as the zero point: a star with magnitude 0 has the same flux as Vega in each filter. Because Vega has a non-flat spectrum, the zero-point flux (in Jy) differs from filter to filter: V-band zero-point is 3636 Jy, J-band is 1589 Jy, K-band is 640 Jy. The AB system uses a flat-spectrum reference source with a constant 3631 Jy at all frequencies: mAB = −2.5 log₁₀(Fν/3631 Jy). SDSS, HST, JWST, and most modern surveys use AB; classical optical photometry (Johnson BVRI) and near-infrared photometry (2MASS JHK) use the Vega system.

The Pogson ratio (101/2.5 = 2.512) is the flux factor per magnitude step. A one-magnitude difference means one source is 2.512 times brighter than the other. Five magnitudes = exactly 100× in flux. The minus sign in the formula ensures the convention that brighter = smaller magnitude, matching the ancient Greek system in which first-magnitude stars were brightest and sixth-magnitude stars were the faintest visible to the naked eye.

📐 Formula

m  =  −2.5 log₁₀(Fν / F0)
m = apparent magnitude (dimensionless; smaller = brighter)
Fν = spectral flux density (Jy = 10−26 W/m²/Hz)
F0 = zero-point flux density for the chosen system and filter
AB system: F0 = 3631 Jy (constant for all filters)
Vega system: F0 = 3636 Jy (V), 4063 Jy (B), 1790 Jy (U), 3064 Jy (R), 2416 Jy (I), 1589 Jy (J), 1021 Jy (H), 640 Jy (K)
Inverse: Fν = F0 × 10−m/2.5
Flux ratio to Δm: Δm = m₂ − m₁ = −2.5 log₁₀(F₂/F₁)
Unit conversions: 1 Jy = 10−26 W/m²/Hz = 10−23 erg/s/cm²/Hz

📖 How to Use This Calculator

Steps

1
Select a conversion mode — Magnitude to Flux converts an apparent magnitude to flux density. Flux to Magnitude converts a flux (Jy, mJy, μJy, nJy) to an apparent magnitude. Flux Ratio converts between flux ratios and magnitude differences.
2
Choose the magnitude system and filter — Select AB (SDSS, HST, JWST) or Vega (Johnson, 2MASS). Then choose the filter bandpass (V is most common for optical, J/H/K for near-infrared).
3
Use a preset or enter a value — Click Sun, Sirius, Vega, Naked-eye limit, or HST limit to load that object's standard V-band magnitude, or type any value.
4
Read the results — Flux outputs are shown in Jy, W/m²/Hz, and erg/s/cm²/Hz. The zero-point and effective wavelength are shown for reference.

💡 Example Calculations

Example 1 — Vega in the V-band (defines the Vega zero point)

Vega: m = 0.03 (Vega system, V-band)

1
V-band Vega zero-point: F0 = 3636 Jy. Magnitude: m = 0.03 (Vega has m = 0.03 rather than exactly 0 due to calibration refinements).
2
Fν = 3636 × 10−0.03/2.5 = 3636 × 10−0.012 = 3636 × 0.97268 = 3536 Jy
3
In SI units: 3536 Jy × 10−26 W/m²/Hz = 3.536 × 10−23 W/m²/Hz
4
In CGS: 3536 Jy × 10−23 erg/s/cm²/Hz = 3.536 × 10−20 erg/s/cm²/Hz
V-band flux of Vega = 3,536 Jy (3.536 × 10−23 W/m²/Hz)
Try this example →

Example 2 — The Sun in the V-band

Sun: m = −26.74 (Vega system, V-band)

1
V-band zero-point: F0 = 3636 Jy. Solar V-band magnitude: m = −26.74
2
Fν = 3636 × 10−(−26.74)/2.5 = 3636 × 10+10.696 = 3636 × 4.966 × 1010 = 1.805 × 1014 Jy
3
Magnitude difference from Vega to Sun: Δm = −26.74 − 0.03 = −26.77 mag. Flux ratio: 1026.77/2.5 = 1010.708 = 5.10 × 1010 (Sun is 51 billion times brighter than Vega in V-band)
4
Faintest HST object (m = 31 AB): F = 3631 × 10−31/2.5 = 1.45 × 10−9 Jy = 1.45 nJy. The Sun is 1.24 × 1023 times brighter than the HST detection limit.
Sun V-band flux ≈ 1.8 × 1014 Jy
Try this example →

Example 3 — Flux Ratio: 5 Magnitudes = Factor of 100

Δm = 5 magnitudes ↔ flux ratio F₁/F₂ = 100

1
Pogson's rule: 5 magnitudes = exactly 100× in flux. F₂/F₁ = 10−Δm/2.5 = 10−5/2.5 = 10−2 = 0.01 (source 2 is 100× fainter than source 1).
2
1 magnitude step: F₂/F₁ = 10−1/2.5 = 10−0.4 = 0.3981. So source 2 is 2.512× fainter (Pogson ratio).
3
Sirius (m=−1.46) vs. Vega (m=0.03): Δm = 0.03 − (−1.46) = 1.49. F(Sirius)/F(Vega) = 101.49/2.5 = 100.596 = 3.94. Sirius is about 3.94 times brighter than Vega in V-band.
4
Naked-eye limit (m=6.5) vs. Vega (m=0.03): Δm = 6.47. F(Vega)/F(limit) = 106.47/2.5 = 102.588 = 387. Vega is 387 times brighter than the faintest naked-eye star.
Δm = 5 ↔ flux ratio = 100.0 (exact by Pogson's definition)
Try this example →

❓ Frequently Asked Questions

What is the difference between the AB and Vega magnitude systems?+
The Vega system sets the zero-point using Vega's measured flux in each filter. Because Vega has a non-flat spectrum, the zero-point flux varies with filter (V: 3636 Jy, J: 1589 Jy, K: 640 Jy). The AB system uses a flat-spectrum reference with a constant 3631 Jy at all frequencies, making cross-filter comparisons simpler. Modern surveys (SDSS, HST, JWST) use AB; classical Johnson photometry and 2MASS use Vega. Converting between them requires filter-specific offsets ranging from about -0.02 mag (V-band) to +1.85 mag (K-band).
What is a Jansky?+
A Jansky (Jy) is the standard unit of spectral flux density in astronomy. 1 Jy = 10^-26 W/m^2/Hz = 10^-23 erg/s/cm^2/Hz. Named after Karl Jansky who discovered cosmic radio emission in 1933. In optical astronomy, mJy and μJy are common. JWST reaches sensitivities of a few nJy. Sub-units: 1 Jy = 10^3 mJy = 10^6 μJy = 10^9 nJy. The Jansky is a per-Hz unit (spectral flux density), not a bolometric (total power) unit.
Why do brighter stars have smaller (more negative) magnitudes?+
The ancient Greek astronomer Hipparchus ranked stars from 1 (brightest) to 6 (faintest visible to the naked eye). When Pogson formalized the scale in 1856 by tying it to flux ratios, he kept the inverted convention. The formula m = -2.5 log(F/F0) gives negative magnitudes for very bright sources because log(F/F0) is large and positive. The Sun at m = -26.74 is 58 magnitudes brighter than the HST limit at m = +31, corresponding to a flux ratio of 10^(58/2.5) = 10^23.
How bright can JWST see and what flux is that in Jy?+
JWST achieves a 5-sigma point-source detection limit of about 28-31 AB magnitude in deep imaging depending on exposure time and filter. At 31 AB: F = 3631 * 10^(-31/2.5) = 1.45 nJy. At 29 AB: F = 9.1 nJy. These correspond to galaxies near the edge of the observable universe (z > 10). The first JWST deep field images revealed thousands of galaxies in a patch of sky smaller than a grain of sand held at arm's length.
What are the UBVRIJHK filters?+
UBVRIJHK is the standard set of photometric filters: U (ultraviolet, 365 nm), B (blue, 440 nm), V (visual, 550 nm), R (red, 640 nm), I (near-IR, 800 nm) are the Johnson optical filters. J (1220 nm), H (1630 nm), K (2190 nm) are the near-infrared 2MASS filters. The V-band corresponds roughly to human visual sensitivity and is the most common reference. Colors like B-V or V-K encode information about stellar temperature, distance, and dust extinction.
What is the Pogson ratio?+
The Pogson ratio is the flux ratio per one magnitude step: 10^(1/2.5) = 10^0.4 = 2.51189... This comes from Pogson's 1856 definition that 5 magnitudes equal exactly 100 in flux: (flux ratio)^5 = 100, so flux ratio = 100^(1/5) = 10^(2/5). Each magnitude step thus corresponds to a factor of 2.512 in flux. Five magnitude steps give exactly 100 times in flux. Ten magnitude steps give 10,000 times. The minus sign in the formula ensures brighter objects (more flux) have smaller magnitudes.
How do I convert between AB and Vega magnitudes?+
The conversion offset varies by filter because Vega has a non-flat spectrum. Approximate offsets (m_Vega = m_AB + offset): U: -0.79 (Vega U magnitudes are 0.79 mag smaller/brighter than AB), B: +0.09, V: -0.02, R: +0.21, I: +0.45, J: +0.91, H: +1.39, K: +1.85. These offsets reflect that Vega is redder than the flat AB reference: in blue bands they are nearly the same, in red and infrared bands Vega has much less flux than the AB reference so a given Vega magnitude corresponds to a fainter (larger) AB magnitude.
What is the spectral flux density versus the total (bolometric) flux?+
Spectral flux density (F_nu in W/m^2/Hz or Jy) is flux per unit frequency interval. Apparent magnitudes are always defined in a specific filter bandpass — they measure spectral flux density averaged over the filter. Total (bolometric) flux integrates F_nu over all frequencies: F_bol = integral(F_nu d_nu). Converting a filter magnitude to bolometric luminosity requires a bolometric correction that accounts for the fraction of the star's total energy emitted outside the filter bandpass. For the Sun in V-band, the bolometric correction is about -0.07 mag — most of the Sun's energy is in the visible.
How is flux density used in multi-wavelength astronomy?+
Multi-wavelength astronomy measures the same object across radio, infrared, optical, UV, X-ray, and gamma-ray bands. Expressing all measurements in flux density (Jy, erg/s/cm^2/Hz, or nW/m^2/sr) on a single spectral energy distribution (SED) plot allows direct comparison of how much energy is emitted at each frequency. SEDs reveal the emission mechanisms (synchrotron, thermal, blackbody, line emission), dust temperature, redshift, and luminosity. The conversion between magnitudes and flux densities is essential for combining data from different surveys and instruments.
What is the surface brightness and how does it differ from apparent magnitude?+
Apparent magnitude characterizes a point source (or the integrated light of an extended source). Surface brightness characterizes extended sources (galaxies, nebulae) as magnitude per square arcsecond (mag/arcsec^2) or as flux per solid angle (Jy/sr or MJy/sr). A galaxy might have apparent magnitude +10 but a surface brightness of +22 mag/arcsec^2 spread over many square arcminutes. The flux-density-per-solid-angle (intensity) is conserved with distance for extended sources (unlike apparent magnitude which gets fainter), making surface brightness a useful intrinsic property for galaxies.
Tags: Flux Density Converter Apparent Magnitude Calculator Jansky to Magnitude AB Magnitude Vega Magnitude UBVRIJHK Filters Calculator Formula Free Online

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What is the difference between the AB and Vega magnitude systems?

The Vega system defines the zero point using the star Vega: a star with magnitude 0 has the same flux as Vega in that filter. Because Vega has different flux densities at different wavelengths, the zero-point flux (in Jy) is filter-dependent (U: 1790 Jy, B: 4063 Jy, V: 3636 Jy, R: 3064 Jy, I: 2416 Jy, J: 1589 Jy, H: 1021 Jy, K: 640 Jy). The AB system uses a flat-spectrum reference source with a constant 3631 Jy at all frequencies, making it easier to work with: m_AB = -2.5 log(F_nu/3631 Jy). Modern surveys (SDSS, HST, JWST) use AB.

What is a Jansky and how does it relate to other flux units?

A Jansky (Jy) is the standard unit of spectral flux density in radio and infrared astronomy. 1 Jy = 10^-26 W/m^2/Hz = 10^-23 erg/s/cm^2/Hz. It is named after Karl Jansky who discovered cosmic radio emission in 1933. For optical work, mJy (millijansky = 10^-3 Jy) and μJy (microjansky = 10^-6 Jy) are common. JWST can detect sources at a few nJy (nanojansky = 10^-9 Jy). The Jansky is a spectral (per-Hz) unit, unlike the bolometric flux in W/m^2 which integrates over all frequencies.

How do I convert between the AB and Vega systems?

A conversion offset exists for each filter because Vega has a non-flat spectrum. In V-band, AB and Vega magnitudes are nearly identical (offset ~ -0.02 mag). In U-band, Vega magnitudes are about 0.79 mag brighter than AB. In K-band, Vega magnitudes are about 1.85 mag brighter than AB (because Vega is much redder than the flat AB reference in the near-infrared). The conversion is m_Vega = m_AB + offset_filter, where offsets are published for each filter/system combination.

What is the pogson ratio and why is 2.512 special?

Norman Pogson formalized the magnitude scale in 1856 by defining a difference of 5 magnitudes to correspond to a factor of exactly 100 in flux. This gives the magnitude step (Pogson ratio) = 100^(1/5) = 10^(2/5) = 10^0.4 = 2.5119... . So each magnitude step corresponds to a flux ratio of approximately 2.512. The formula m = -2.5 log(F/F0) encodes this: a 1-magnitude change means F changes by 10^(2.5/2.5) = 10^1 ... no wait: for dm=1, F2/F1 = 10^(-1/2.5) = 10^(-0.4) = 0.3981, or equivalently the brighter source is 2.512x more flux. The minus sign means brighter objects have smaller (more negative) magnitudes.

What does it mean for a source to have magnitude -26 or +31?

The apparent magnitude scale is reversed: lower numbers mean brighter. The Sun has V = -26.74, making it the brightest object in the sky by far. Sirius is -1.46, Vega is about 0.03, the faintest stars visible to the naked eye under perfect conditions are about +6.5, typical binoculars reach +10, amateur telescopes +13 to +15. The Hubble Space Telescope can detect objects at +31 in deep imaging. JWST reaches +31 in infrared. The full dynamic range from the Sun to the JWST limit is about 58 magnitudes, corresponding to a flux ratio of 10^(58/2.5) = 10^23.

What is flux density versus flux and why does it matter?

Flux is the total power per unit area received across all wavelengths (W/m^2), the bolometric quantity. Flux density (also called specific flux) is flux per unit frequency (W/m^2/Hz) or per unit wavelength (W/m^2/nm). Apparent magnitudes are defined in terms of spectral flux density in a specific filter bandpass, not bolometric flux. The Jansky is a spectral flux density unit. Bolometric corrections convert filter-band magnitudes to total (all-wavelength) luminosities, but they require knowing the source spectrum.

What magnitude can JWST detect and what does that correspond to in Jy?

JWST can detect sources at about 29-31 AB magnitude in deep imaging depending on exposure time and filter. At 31 AB: F = 3631 * 10^(-31/2.5) Jy = 3631 * 10^(-12.4) = 3631 * 3.98e-13 = 1.45e-9 Jy = 1.45 nJy. At 29 AB: F = 3631 * 10^(-11.6) = 3631 * 2.51e-12 = 9.1e-9 Jy = 9.1 nJy. These are roughly the flux densities of galaxies near the edge of the observable universe. The Sun at 10 parsecs has V ≈ 4.8, corresponding to ~3560 Jy at 10 pc — 13 orders of magnitude brighter than the JWST limit.

How does the filter bandpass affect the conversion?

Each filter only transmits a range of wavelengths. A magnitude measured through a filter captures only the flux in that wavelength range. The zero-point flux F0 is defined as the flux density of a zero-magnitude source in that filter, set by the Vega spectrum (Vega system) or by the flat-spectrum reference (AB system). Comparing magnitudes in different filters reveals the spectral energy distribution (color) of the source. For example, V-J color measures the flux ratio between visible and near-infrared, correlating with stellar temperature.

How do I use magnitude differences to compare star brightnesses?

The formula Δm = m2 - m1 = -2.5 log(F2/F1) gives the magnitude difference from a flux ratio, or equivalently F2/F1 = 10^(-Δm/2.5). To compare brightness: if Star A has m=1 and Star B has m=6, then Δm=5 and F_A/F_B = 10^(5/2.5) = 100: Star A is 100 times brighter. If Δm=-1 (Star A fainter), F_A/F_B = 10^(-(-1)/2.5) = 10^0.4 = 2.512. The ratio mode in this calculator lets you enter either two flux densities or a magnitude difference to find the other.

What is the V-band and what do UBVRIJHK stand for?

UBVRIJHK is the standard photometric filter system. U (ultraviolet, 365 nm), B (blue, 440 nm), V (visual, 550 nm), R (red, 640 nm), I (infrared, 800 nm) are the Johnson optical filters. J (1220 nm), H (1630 nm), K (2190 nm) are the near-infrared 2MASS filters. The V-band was historically chosen to match human visual perception. B-V color (blue minus visual magnitude) is a measure of stellar temperature: hot blue stars have B-V ~0, cool red stars have B-V ~1.5.

Why are some sources measured in mJy or μJy rather than Jy?

Astronomical sources span an enormous flux range. Bright radio sources like Cassiopeia A have flux densities of thousands of Jy at 1 GHz. The brightest optical stars are tens of thousands of Jy. But distant galaxies and faint radio sources are measured in mJy to nJy. VLBI and interferometric radio surveys reach micro-Jy sensitivities. Using sub-units (mJy, μJy, nJy) avoids writing many zeros and makes comparisons intuitive. For reference: 1 Jy = 10^3 mJy = 10^6 μJy = 10^9 nJy.

📌 Quick Tips

💡The AB magnitude system uses a constant zero-point of 3631 Jy regardless of filter: m_AB = -2.5 log(F_ν/3631 Jy). This makes it easy to compare fluxes across different filters without memorizing filter-specific zero-points.
💡Vega defines the zero point: Vega has magnitude 0.03 in the V-band (not exactly 0 because Vega was re-measured after the original calibration). The Vega V-band zero-point is approximately 3636 Jy.
💡A factor of 100 in flux corresponds to exactly 5 magnitudes. Each magnitude step corresponds to a flux ratio of 10^(1/2.5) = 2.512... (the Pogson ratio).
💡Modern photometric surveys (SDSS, HST, JWST) mostly use the AB system. Older optical photometry (BVRI) uses the Vega system. Near-IR (JHK) photometry often uses a Vega-based 2MASS system.
💡JWST can detect objects down to about 31 AB magnitude in deep exposures — equivalent to about 2 nJy, or roughly 10 billion times fainter than the faintest star visible to the naked eye.