Magnitude & Brightness Calculator

Convert between apparent magnitude difference and brightness (flux) ratio using F1/F2 = 10^(-0.4(m1-m2)) — with a two-star visual comparison and a magnitude number line to make the reversed, logarithmic scale intuitive.

Magnitude / brightness calculator

The magnitude scale runs backwards and logarithmically: lower (or more negative) means brighter, and every 5 magnitudes is exactly a factor of 100 in flux — F₁/F₂ = 10^(−0.4·(m₁−m₂)). Convert a magnitude difference into a brightness ratio, or flip it around and enter a ratio to get the magnitude difference it implies.

Object A magnitude (m_A)

Object B magnitude (m_B)

Object A appears 100× brighter

Δm = m_A − m_B = -5.00

Symbol size (and glow) scales linearly with magnitude, the same convention used on real star charts — so both objects stay visible on screen no matter how extreme the true ratio is. The exact factor is always given as a number, above and below.

Magnitude increases to the right — the opposite of most numeric scales — so the physically brighter object always sits on the left, however negative its number is.

ΔmBrightness ratio

12.512×

26.31×

2.510×

5100×

7.51000×

1010000×

151 × 10⁶×

201 × 10⁸×

Astronomers rank how bright things look with a scale that runs backwards: a lower number means brighter, negative numbers exist, and each step is a multiplication, not an addition. None of that is obvious the first time you meet it. This calculator converts between a magnitude difference and the brightness ratio it represents, in either direction, and draws both quantities so the logic behind the scale becomes something you can see rather than something you have to memorize.

Why the scale is backwards and logarithmic

Magnitude dates back to Hipparchus ranking stars by eye around 150 BCE: the brightest stars were “first magnitude,” the faintest visible ones “sixth magnitude” — a ranking, not a measurement, which is why brighter means lower. In 1856 Norman Pogson formalized the old ranking into a precise scale by noting that first-magnitude stars are about 100 times brighter than sixth-magnitude ones, and defining the scale so that’s exact:

\frac{F_1}{F_2} = 10^{-0.4(m_1 - m_2)}

Every 5 magnitudes is a factor of exactly 100 in flux, so every single magnitude is a factor of 100^(1/5) ≈ 2.512 — the Pogson ratio. Two objects with magnitudes 2 and 7 differ by 5, so the magnitude-2 object is exactly 100× brighter; that’s the example baked into this calculator’s default values.

Running it in reverse

The same relation solves the other way just as easily. Given a flux ratio F1/F2, the magnitude difference it implies is

m_1 - m_2 = -2.5 \log_{10}\left(\frac{F_1}{F_2}\right)

Switch the calculator to “Ratio → Magnitude difference,” enter something like “10× brighter,” and it returns Δm ≈ −2.5 — useful for going from a brightness comparison you can picture (a lamp ten times brighter than another) to the number a star catalog would actually print.

Making a logarithmic, reversed scale visual

Two charts do the intuition work here:

The two-star comparison sizes each object’s symbol linearly by magnitude — the same convention real star charts use — rather than linearly by flux. True flux ratios routinely span many orders of magnitude (the Sun is about $10^14$ times brighter than the faintest star your eye can see), so a size scaled directly to flux would make one star vanish in almost every realistic comparison. Sizing by magnitude instead keeps both symbols visible while still shrinking monotonically as the true ratio grows — the exact factor is always given as a number alongside it, never left for the eye alone to judge.
The magnitude number line plots both objects on a single axis that increases left to right — meaning the physically brighter object always lands on the left, however negative its magnitude is. Seeing Sirius (−1.46) sit left of Polaris (+1.98) on a line labeled “brighter → dimmer” does more to fix the reversed convention in memory than the rule stated in words ever does.

A few reference points

Δm = 1 → 2.512× (the Pogson ratio itself)
Δm = 2.5 → exactly 10×
Δm = 5 → exactly 100×
Δm = 10 → exactly 10,000×
Sirius vs. Polaris (Δm ≈ 3.44) → about 24× brighter
Full Moon vs. faintest naked-eye star (Δm ≈ 19.2) → about 48 million times brighter

The calculator’s built-in presets reproduce each of the worked examples above — the reference table underneath the charts highlights whichever row your current Δm is closest to.