Atmospheric Refraction Angle Calculator
Find how much Earth's atmosphere bends light near the horizon, using Saemundsson's classic refraction formula.
🌅 What is Atmospheric Refraction?
Atmospheric refraction is the bending of light as it passes through Earth's atmosphere, caused by the gradual change in air density from the ground up to space. Because the atmosphere is denser near the surface, light rays curve slightly downward as they travel through it, which makes celestial objects appear higher in the sky than their true geometric position, an effect that grows dramatically stronger the closer an object is to the horizon.
Astronomers apply refraction corrections when pointing telescopes precisely at low-altitude targets. Celestial navigators historically corrected sextant sightings for refraction to get an accurate position fix at sea. Photographers and sky-watchers notice refraction directly every time they see the Sun or Moon look flattened and oval-shaped near the horizon. Surveyors working with very long sight lines near ground level also account for atmospheric refraction, since it bends light over land the same way it bends light from the sky.
A common misconception is that refraction only matters for astronomers with telescopes. In reality, it is visible to the naked eye every clear sunrise and sunset, refraction is the reason the Sun appears to still be above the horizon for a few extra minutes after it has geometrically already set.
This calculator applies Saemundsson's (1986) refraction formula, accurate to about 0.07 arcminutes across the full range from the horizon to the zenith, to compute the refraction angle and the resulting true altitude from any entered apparent altitude.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Right at the Horizon
h = 0° (setting Sun touching the horizon)
Example 2 — Low in the Sky
h = 5°
Example 3 — Well Above the Horizon
h = 45°
❓ Frequently Asked Questions
🔗 Related Calculators
What is the formula for atmospheric refraction?
Saemundsson's (1986) formula gives refraction in arcminutes as R = 1.02 / tan(h + 10.3/(h+5.11)), where h is the apparent altitude in degrees and the argument of the tangent is also in degrees. It is accurate to about 0.07 arcminutes from the horizon to the zenith under standard atmospheric conditions.
How much does the atmosphere bend light at the horizon?
At an apparent altitude of exactly 0 degrees (right at the horizon), Saemundsson's formula gives a refraction of about 29 arcminutes, close to the Sun's own angular diameter. This is why the setting Sun appears to touch the horizon several minutes before it has actually geometrically set.
How do I find the true (geometric) altitude of an object?
Subtract the refraction from the apparent altitude, converting arcminutes to degrees first: true altitude = h - R/60. At h = 5 degrees, for example, R is about 9.67 arcminutes, so the true altitude is about 4.84 degrees, roughly 0.16 degrees lower than what is observed.
Why does the setting Sun look flattened or oval?
The bottom edge of the Sun's disk is closer to the horizon than the top edge, so it experiences noticeably more refraction and is bent upward more strongly. That differential bending compresses the vertical dimension of the disk, producing the familiar flattened, oval look during sunrise and sunset.
Does refraction delay sunset?
Yes. Because refraction bends light from an object that is geometrically just below the horizon up into view, sunrise appears to happen slightly earlier and sunset slightly later than a purely geometric calculation would predict, typically by a few minutes at temperate latitudes.
Is refraction the same at every altitude?
No. Refraction is largest at the horizon, roughly half a degree, and decreases rapidly as altitude increases, dropping below about 1 arcminute by 45 degrees and becoming essentially zero at the zenith (90 degrees), where light passes straight through the atmosphere without bending.
What assumptions does Saemundsson's formula make?
It assumes standard atmospheric conditions of about 1010 hPa pressure and 10 degrees C temperature. Actual refraction varies somewhat with real barometric pressure and temperature, since both affect air density and therefore how strongly light bends, so precise applications apply an additional pressure and temperature correction factor.
Who developed the formula this calculator uses?
Thorsteinn Saemundsson published this widely used approximation in 1986, building on earlier refraction formulas including one by George Bennett in 1982. Saemundsson's version is commonly cited for its simplicity and accuracy across the full range of altitudes from the horizon to the zenith.
Why is the formula's tangent argument converted from degrees to radians in code?
Saemundsson's formula is defined with its angle in degrees, but JavaScript's Math.tan function (like most programming languages) expects radians. The angle (h + 10.3/(h+5.11)), computed in degrees, must be multiplied by pi/180 to convert it to radians before calling Math.tan, otherwise the result is meaningless.
Does refraction matter for everyday stargazing?
Yes, especially near the horizon. Objects you see rising or setting, including stars, planets, the Moon, and the Sun, appear noticeably higher in the sky than their true geometric position whenever they are within a few degrees of the horizon, which matters for precise pointing with a telescope or for timing rise and set events.