Why the sky is blue and sunsets are red

Look up on a clear afternoon

Sunlight is white, and the air it shines through is clear. So where does a blue sky come from, and why does the same sun look orange half an hour before it sets? Both colours come from one effect. Air molecules knock a little of the sunlight off course, and they do it much more to short wavelengths than to long ones.

The model above is a field under a sky that is calculated, pixel by pixel, from that effect. You can drag the sun down to the horizon, thicken the haze, put a volcanic layer in the stratosphere, lift your eye to an airliner's cruising height or to orbit, and swap the planet for Mars, the Moon, Uranus or Neptune. The panel on the left gives the numbers behind each picture, and the bar along the bottom sets up 23 real conditions in one tap.

Why air scatters blue more than red

A molecule of nitrogen or oxygen is about a thousand times smaller than the wavelength of visible light. When a light wave passes, it pushes the molecule's electrons back and forth, and the jiggling electrons send out light of their own in almost every direction. This is Rayleigh scattering, and its strength goes as one over the wavelength to the fourth power.

The fourth power is what makes it so lopsided. Blue light at 440 nm has a wavelength 0.65 times that of red light at 680 nm, and 0.65⁴ is about 0.18, so blue is scattered roughly 5.7 times more. Using the measured refractive index of air, which is itself a little higher for blue, the model gets 5.9. Over the whole visible range, from 400 to 700 nm, the ratio is almost 10.

In numbers, a vertical column of clean air scatters out about 19% of the 450 nm light that enters it, and under 5% of the 650 nm light. That missing blue does not vanish. It is spread across the whole dome of the sky, and that is the light you see when you look away from the sun.

Turn on Eye sensitivity and the chart in the panel shows two curves together: the spectrum of light reaching the centre of your view (rising toward the violet end) and the eye's own sensitivity (a hump centred on green).

Why the sky is blue and not violet

If short wavelengths scatter most, the sky ought to be violet. The model's spectrum for the sky overhead does in fact peak at the violet end of the visible range, near 380 nm. Three things stop us from seeing violet.

First, sunlight itself has less violet than blue to start with, and some of the ultraviolet and violet is absorbed high up. Second, the eye is very poor at violet: its sensitivity at 400 nm is about 0.1% of its peak at 555 nm, against 3% at 450 nm. Weighted by the eye, the sky spectrum peaks near 540 nm. Third, colour is not read off the peak at all. The three kinds of cone each respond to a broad band, and the mix that skylight produces sits closest to a pale blue. The model turns the computed spectrum into a colour the same way, and the dominant wavelength comes out at 478 nm, a sky blue.

So the sky's colour is a mixture with a strong blue excess, not a single wavelength. That is also why it is never as saturated as a laser or a rainbow.

A low sun shines through far more air

The second half of the story is geometry. When the sun is overhead, its light crosses one thickness of atmosphere, which you can think of as an 8 km layer of air at sea-level density. When the sun is lower, the slanted path is longer. The ratio of the two is called the air mass.

The "1 over the sine of the height" rule works well down to about 10°, then fails badly because the Earth is round: it would give infinity at the horizon. The model follows the curved layer instead and gets 35 at the horizon. The widely used Kasten and Young formula, fitted to real refraction, gives 38.

Where the red and orange come from

Each air mass scatters out the same fraction of each colour, so the losses multiply. With clean air and a little haze, here is how much of the direct sunlight is left at two wavelengths:

At 5° the red light is seven times stronger than the blue, relative to what left the sun. The disc turns orange, then red, and it is much dimmer, which is why you can sometimes look at a setting sun that would hurt your eyes at noon. Press Play and the sun sinks at about 2° a second, and the white line in the chart sags at the blue end as it goes.

The clouds and the sky near the sun take on the same colour because they are lit by the same reddened light. Higher clouds stay lit for longer after sunset, which is why they glow after the ground is in shade.

After sunset: the shadow, the belt and the blue hour

Turn around after the sun has gone down and look at the opposite horizon. A grey-blue band lies along it: the shadow of the Earth itself, cast on the air. Above it is a pink band, the Belt of Venus, where the air is high enough to still catch the red light of the sun that has already set for you. As the sun sinks further, the shadow rises and the belt fades.

You might expect the sky to go grey as twilight deepens, since the sunlight lighting the upper air has crossed so much of the lower atmosphere that it is very red. Instead it turns a deep blue. The reason is ozone. Its Chappuis band absorbs orange and yellow light around 600 nm, weakly from overhead (the model gives an optical depth of 0.04), but strongly along the very long, nearly horizontal path that twilight light takes through the ozone layer. Pick Blue hour to see the sun 6° below the horizon.

What haze, dust and smoke change

Particles much bigger than molecules behave differently. Droplets, dust and smoke are a tenth of a micrometre up to several micrometres across, close to the wavelength of light or larger. They scatter all colours more evenly, and they send most of their light forward, into a few degrees round the sun. That forward scattering is the white glare round the sun on a hazy day.

The model describes haze with two numbers. Haze and fine dust is the aerosol optical depth at 550 nm, the quantity measured by sun photometers in the AERONET network. Clean country air is below 0.1; a polluted day in a big city can go past 1. Particle size is the Ångström exponent: about 2 for fine smoke, which still favours blue a little, and near 0 for coarse desert dust, which scatters all colours alike.

More haze has two visible effects. Far hills fade into grey-blue, since the air between you and them adds its own light: painters call this aerial perspective. And the sunset gets dimmer rather than redder, because with an optical depth of 0.8 and the sun at 5°, almost nothing of any colour gets through. The brightest red sunsets come from clean air with a thin haze, not from heavy pollution.

Smoke is the exception that proves the rule. In September 2020 smoke from wildfires on the US west coast was so thick that its optical depth passed 5 in places, enough to darken the daytime sky. Pick Wildfire smoke to set an optical depth of 3 with small particles.

Volcanoes high up

A large eruption can lift sulphur dioxide above the weather into the stratosphere, where it turns into tiny droplets of sulphuric acid. They spread round the planet and stay for a year or more. Mount Pinatubo, in the Philippines, did this in June 1991, and the haze cooled the planet by about 0.5 °C until 1993.

The layer sits at about 20 km, so it stays in sunlight for a while after the ground goes dark. Turn on Volcanic haze layer and set the sun 3° below the horizon: a pink and purple glow appears high above the afterglow. After the eruption of Krakatoa in 1883 the twilight colours were so strong that fire engines were called out in New York, Poughkeepsie and New Haven to fight fires that did not exist.

Going higher

Air thins with height. In the model's atmosphere the density halves about every 5.5 km. Eye height moves you up, and the sky overhead darkens because there is less air above you to scatter light.

At 4,000 m on a mountain, about 40% of the air is below you and the zenith is a deep, dark blue. At 10,700 m, a normal airliner cruise, three quarters of the air is below, and through the window the sky overhead is navy while the horizon is still pale. Concorde cruised at up to 18,300 m, where its passengers could see the sky darken above a bright band. At 39 km, the height of Felix Baumgartner's jump in 2012, less than 1% of the air is above you and the sky is black even at midday.

From the International Space Station, about 400 km up, the atmosphere is a thin glowing line along the curved edge of the planet. The blue is still there, but now you see it from the side.

Other skies

Mars has an atmosphere of carbon dioxide with a surface pressure of 6.36 millibars, less than 1% of ours, so its gas scatters very little. What colours the sky is fine dust that is always in the air. The dust absorbs blue light (it contains iron oxides) and scatters red widely, so the daytime sky is a yellow-brown that people call butterscotch. In the model, at 45° from the sun the sky is 27% weaker in blue than in red.

At sunset the picture flips. Dust grains a little larger than the wavelength of light throw blue light forward into a narrower cone than red, so close to the sun the scattered light is bluer. The model gives a blue glow round the setting sun with 44% more blue than red, matching the photograph the Curiosity rover took in Gale crater in April 2015. In the 2018 global dust storm the optical depth at Opportunity's site passed 10. The solar-powered Opportunity rover lost power and never woke again.

The Moon has no air, so nothing is scattered and the sky is black with the sun high up. The ground is lit by the sun alone.

Uranus and Neptune have no solid surface, so in the model you float above the methane cloud deck. Hydrogen and helium scatter blue like our air, and methane absorbs red light strongly, so the light that comes back out is green-blue. A 2024 study from Oxford, which rebalanced the Voyager 2 and Hubble images, found the two planets are a similar pale greenish blue. Neptune is a little bluer because its haze layer is thinner. The deep blue Neptune in older pictures came from contrast-stretched images.

Twenty-three conditions to try

The bar under the model sets up each case and points the view at the interesting part of the sky.

1. Clear noon: sun 65° up, a deep blue overhead.
2. Afternoon: 30° up, the horizon fading toward white.
3. Golden hour: 6° up, warm light on the field.
4. Sunset: half a degree up, the disc red and dim.
5. Earth's shadow: 2.5° below, looking east.
6. Blue hour: 6° below, ozone keeping the twilight blue.
7. After rain: optical depth 0.01, far hills sharp.
8. Hazy day: optical depth 0.8, hills faded.
9. Yellow dust: optical depth 1.5 of coarse grains from the desert.
10. Wildfire smoke: optical depth 3, an orange day.
11. After Pinatubo: sulphate layer of optical depth 0.15.
12. After Krakatoa: a thicker layer, 0.35.
13. Mountain top: eye at 4,000 m.
14. Airliner window: eye at 10,700 m.
15. Concorde: eye at 18,300 m.
16. Stratosphere jump: eye at 39 km.
17. Space station: eye at 400 km.
18. Mars by day: dust optical depth 0.6.
19. Mars sunset: the blue glow.
20. Mars dust storm: optical depth 5.
21. Moon: a black sky.
22. Uranus: thick haze, pale green-blue.
23. Neptune: thinner haze, a little bluer.

Checking the colour on screen

The ring in the middle of the view is measured twice. Screen pixel reads the colour actually drawn at that spot, after the exposure and the screen's colour handling. From spectrum takes the model's computed spectrum at the same spot, turns it into CIE colour coordinates with the standard observer, converts that to sRGB and scales it so the brightest channel is full. So the spectrum swatch always shows the hue at full brightness, while the screen pixel also carries the exposure of the whole picture and is usually darker and greyer. Compare the balance of red, green and blue in the two. When the balance differs a lot, the shortcut used for drawing (three wavelengths for red, green and blue) has strayed from the full spectrum.

What the model leaves out

• Light is scattered once. Real skylight is partly scattered two or more times, which brightens the horizon and the twilight sky. The model adds a rough allowance for that.
• Drawing uses three wavelengths, 680, 550 and 440 nm; the chart and the colour check use 35, every 10 nm from 380 to 720 nm.
• Haze has one particle size per condition and sits in a single layer that thins with height. Real haze comes in layers of mixed sizes.
• There are no clouds on Earth, no rainbows and no polarisation, though skylight 90° from the sun is strongly polarised.
• Refraction is ignored, so the sun is not lifted or flattened near the horizon.
• The Uranus and Neptune methane absorption is a smooth fit, not the real band structure.

A short history

In the late 1860s John Tyndall shone strong beams through tubes of fine particles and saw blue light scattered sideways, now called the Tyndall effect. Lord Rayleigh published the theory in 1871, showing that particles much smaller than the wavelength scatter in proportion to 1/λ⁴, and in 1899 he showed that air molecules alone are enough to make the sky blue, with no dust needed. Rayleigh won the 1904 Nobel Prize in physics, for his work on the densities of gases and the discovery of argon. Later, Smoluchowski and Einstein linked the scattering of gases to tiny fluctuations in their density, which closed the last gap in the theory.

The type of model used here, which marches along each view ray through a spherical atmosphere, comes from computer graphics: Nishita and colleagues in 1993, and the precomputed method of Bruneton and Neyret in 2008.

Worked example: the arithmetic of 1/λ⁴

Take blue light at 450 nm and red light at 700 nm. Rayleigh scattering goes as 1/λ⁴, so the ratio of the two strengths is (700 ÷ 450)⁴. The wavelength ratio is 1.556. Squared that is 2.42, and squared again it is 5.86. Blue is scattered about 5.9 times as strongly as red, close to the 5.7 to 5.9 the model gets for the 440 and 680 nm pair it draws with. The pair 380 nm and 700 nm gives (700 ÷ 380)⁴, about 11.5.

Now turn the ratio into what reaches the ground. The model says a vertical column of clean air scatters out about 19% of 450 nm light, so 81% gets through. The loss is written with an optical depth τ, where the fraction surviving is e⁻τ, and 0.81 means τ = 0.21. Scale it by the same 5.86 and the red value is τ = 0.21 ÷ 5.86 = 0.036, so 96% of the 700 nm light survives.

Here is the sunset. At the horizon the air mass is about 38 (Kasten and Young), so the optical depths are multiplied by 38. Blue: 0.21 × 38 = 8.0, and e⁻⁸·⁰ is 0.0003. Red: 0.036 × 38 = 1.4, and e⁻¹·⁴ is 0.25. The sun has lost nearly all of its blue but a quarter of its red, a ratio of about 760 to 1. This is a simplified check that uses air molecules only and treats the 1/λ⁴ law as exact. The model's own numbers also include ozone and haze, so they differ a little, but the story is the same.

Air molecules, droplets and haze: why size matters

Whether light is scattered by 1/λ⁴ depends on the size of the particle compared with the wavelength. A nitrogen molecule is a fraction of a nanometre across, a thousand times smaller than light, so the electrons all move together and Rayleigh's law holds. Haze particles of 0.1 to 1 µm are close to the wavelength, and their scattering is described by Mie theory. Colour dependence weakens, and most of the light goes forward. Cloud droplets of 10 µm or so are about twenty times bigger than the wavelength and scatter every visible colour almost equally, so sunlit cloud is white.

The same idea explains a whitish sky. In a smoggy city or a humid summer the particles add their nearly colourless scattered light to the blue of the molecules, and the sky pales, most of all near the horizon, where the line of sight crosses the most air. Set Haze and fine dust to 0.8 and watch the deep blue turn milky. If you then make Particle size small, the sky keeps some blue. If you make it near 0, as for desert dust, the sky goes grey-white.

On a mountain day after rain the picture reverses. With few particles the sky looks darker and bluer, and the far hills look sharp. This is what the After rain condition shows.

Skylight is polarised

Light scattered from a molecule goes out in all directions, and it is also polarised. In the ideal single-scattering case, light that has turned through exactly 90° is fully polarised, with its electric field vibrating perpendicular to the plane that holds the sun, the molecule and your eye. In the direction of the sun, or directly away from it, it is not polarised. So the clear blue sky at 90° from the sun is the most polarised patch.

Real skylight never quite reaches the ideal. It is scattered more than once, bounces off the ground, and is mixed with haze, all of which lower the polarisation. You can still see it. Put on polarising sunglasses, look at a clear patch of sky 90° from the sun, and tilt your head: the sky brightens and darkens. Tyndall noted the polarisation of skylight in 1869 and Rayleigh worked out its theory in 1871, in the same paper that gives the 1/λ⁴ law. The model leaves polarisation out and draws only the total brightness, so what you see on screen is the sum of the two directions.

Common misunderstandings

"The sky is blue because it reflects the sea." It is the other way round in part. The sky is blue over deserts, mountains and lakes that are not blue at all. The sea is blue because water absorbs red light, so it filters the sunlight and leaves blue, as NOAA explains. The sea can also copy the colour of the sky on its surface, but the two colours have different causes.

"Dust or water vapour makes the sky blue." Tyndall's experiments used fine particles, and dust was long suspected. Rayleigh showed in 1899 that the air molecules alone scatter enough. Clean air is bluer, not less blue.

"The sky is violet but our eyes can't see it." Half right. The eye is weak at violet, and so is sunlight at the top of the atmosphere, but the cones also respond to a broad mixture, and the mixture looks pale blue. The section on violet above has the numbers.

"Ozone makes the sky blue." Ozone has a weak effect in the daytime. Its absorption matters for the blue of deep twilight, where the light crosses a very long path.

"Red sunsets come from pollution." Pollution can make a sunset more orange, but clean air already gives a red sun, because the colour comes from the long path. Very thick smoke gives a dark sun instead.

"Blue light is bent more, so the sun looks red when low." Refraction does bend blue light slightly more, but it plays no real part here. Scattering, not bending, removes the blue.

Try it on screen

1. Pick Clear noon, then Golden hour and Sunset. Watch the Air mass and Light left 680/440 nm rows. The air mass climbs steeply, and the blue share of the direct light falls much faster than the red.
2. Pick Hazy day, then lower the sun by hand. With more haze the sun reddens less and the sunset dims, as in the section on haze.
3. Pick After rain and then Yellow dust. Compare the sky near the horizon and the far hills.
4. Pick Mars by day and Mars sunset. The daytime sky is butterscotch, while the blue glow around the setting sun appears only at sunset.
5. Raise Eye height from the ground up to the Airliner window and the Stratosphere jump, and read how the sky overhead goes from blue to navy to black.
6. Turn on Eye sensitivity and compare the sky curve with the eye curve.