Star Temperature Calculator

Enter the star’s luminosity, radius, and temperature values into the calculator leaving exactly one field empty to determine its missing value.

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Star Temperature Formula

The Stefan-Boltzmann law is the foundational equation for deriving a star's effective surface temperature from its luminosity and radius.

T = \left(\frac{L}{4\pi\sigma R^2}\right)^{\frac{1}{4}}

• Where T is the effective surface temperature (K)
• L is the total luminosity (W)
• R is the stellar radius (m)
• sigma = 5.670374419 x 10^-8 W m^-2 K^-4 (Stefan-Boltzmann constant)

Wien's displacement law provides a complementary route: the peak emission wavelength lambda_max (meters) satisfies lambda_max x T = 2.897771955 x 10^-3 m K. This is the basis for the Wien's Law tab in the calculator. The Flux at Distance tab uses F = L / (4 pi d^2), the inverse-square law for apparent flux received at a distance d from the star.

What Is Stellar Surface Temperature?

Stellar surface temperature, formally called effective temperature (T_eff), is the temperature of an equivalent blackbody radiator emitting the same total power per unit area as the star's photosphere. It is not a measurement of any single atmospheric layer but rather a single representative value integrated from the Stefan-Boltzmann law. The Sun's T_eff is 5,772 K, yet actual photospheric temperatures range from roughly 4,000 K inside sunspot umbrae to over 6,200 K in the bright granule centers. The solar core reaches approximately 15 million K, sustained by hydrogen fusion, which has no bearing on the photospheric T_eff used in this calculator.

Effective temperature is the single most consequential observable property of a star. It determines the ionization state of the photospheric gas, which spectral absorption lines appear and how strong they are, the color of the star as seen from Earth, and the star's position on the Hertzsprung-Russell diagram. A shift of just 250 K at the boundary between spectral subclasses can reorganize which atomic transitions are detectable, changing the classified spectral type entirely.

Spectral Classification and Temperature Ranges

The Morgan-Keenan (MK) system classifies stars using the letter sequence O, B, A, F, G, K, M from hottest to coolest, with each class subdivided 0 through 9 (0 is hotter within the class, 9 is cooler). A second component, the luminosity class (I through VII), distinguishes supergiants from giants, main-sequence stars, and white dwarfs. The Sun's full designation is G2V: a main-sequence (class V) star in the G class at subtype 2, with an effective temperature of 5,772 K.

Beyond the classical OBAFGKM sequence, extended classes include L-type brown dwarfs (1,300 to 2,100 K), T-type methane dwarfs (700 to 1,300 K), and Y-type ultra-cool brown dwarfs below 700 K, with some Y dwarfs approaching room temperature. At the hot extreme, Wolf-Rayet stars (WR class) reach 200,000 K, and newly formed white dwarfs briefly exceed 100,000 K before cooling over billions of years.

Notable Star Temperature Reference

The table below provides verified effective temperatures for ten well-known stars alongside their luminosities and radii in solar units, which can be used directly as inputs in the Stefan-Boltzmann tab of the calculator above.

A useful pattern from the table: Betelgeuse and Rigel are both supergiants with luminosities over 100,000 L_sun, yet their temperatures differ by a factor of 3.5. This illustrates why luminosity class matters as much as spectral type. Both stars are intrinsically more luminous than 99.9% of all stars in the Milky Way despite their contrasting temperatures.

Temperature, Color, and Peak Wavelength

Wien's displacement law creates a direct, predictable link between temperature and the color a star radiates most strongly. A 3,000 K red dwarf peaks near 970 nm in the near-infrared, just beyond the red edge of visible light, so it emits visible light only in the reddest portion of the spectrum. The 5,772 K Sun peaks at about 502 nm (green), but emits across the full visible band and appears white to yellow. A 30,000 K O-type star peaks near 97 nm in the far ultraviolet, making most of its power output invisible to the human eye yet intensely ionizing to surrounding gas clouds.

The B-V color index quantifies this temperature-color relationship photometrically. Hot blue stars have negative B-V values (Rigel: -0.03), while cool red stars have strongly positive values (Betelgeuse: +1.85, Antares: +1.83). The Sun's B-V is +0.656. No main-sequence star appears violet to the naked eye even though O-type stars emit strongly in the violet and UV: Earth's atmosphere absorbs most UV output, and human photoreceptors have limited violet sensitivity, so the perceptual result is blue-white rather than violet.

Star Temperature and Habitable Zone Location

A star's effective temperature, through its effect on luminosity, determines where the circumstellar habitable zone (the orbital range where liquid water can exist on a rocky planet surface) is located. Hotter, more luminous stars push the habitable zone outward. A 10,000 K A-type star like Vega has a habitable zone centered near 8 to 10 AU, roughly equivalent to Saturn's distance from the Sun. The 5,772 K Sun places it between approximately 0.95 and 1.37 AU. A 3,042 K M-dwarf like Proxima Centauri has a habitable zone at only 0.04 to 0.08 AU, well within Mercury's orbit around the Sun, meaning any liquid-water planet there is almost certainly tidally locked with one hemisphere in permanent daylight.

Star temperature also shapes the UV radiation environment, which governs both atmospheric loss rates and photochemistry on planetary surfaces. O and B stars emit UV fluxes many thousands of times higher than the Sun, capable of eroding atmospheres and dissociating water vapor. F-type stars emit moderately elevated UV compared to the Sun while still offering wide habitable zones and multi-billion year lifetimes, making them targets in exoplanet habitability research. M-dwarf habitable zones are close enough that stellar flares can deliver intense UV bursts to orbiting planets even though the quiescent surface temperature is low.

How Stellar Temperature Changes Over Time

A star's effective temperature is not static across its lifetime. The Sun is approximately 30% more luminous today than it was at formation 4.6 billion years ago, and its T_eff has risen correspondingly. On the main sequence this change is slow. As a solar-mass star exhausts core hydrogen and expands into a red giant, its surface temperature drops from around 5,800 K to roughly 4,000 to 5,000 K despite a luminosity increase of 100 to 1,000 times, because the enormous radius expansion dominates the T formula: more area radiating at lower temperature can still produce more total power.

White dwarfs form at surface temperatures above 100,000 K and cool passively over billions of years. The current universe is not old enough for any white dwarf to have cooled below about 3,800 to 4,000 K, so a purely theorized cold black dwarf does not yet exist anywhere. The coolest known white dwarfs are around 3,900 K and appear orange-red. Neutron stars form during supernovae with surface temperatures of 100 billion K or more, cooling to roughly 1 million K within the first century, then more slowly over millions of years.

FAQ

What is stellar effective temperature?

Effective temperature (T_eff) is the temperature of a blackbody with the same luminosity per unit surface area as the star. It is derived from the Stefan-Boltzmann law and serves as the standard single-value descriptor of a star's photospheric thermal output. The Sun's T_eff is 5,772 K.

How does temperature relate to a star's spectral class?

The OBAFGKM sequence is fundamentally a temperature sequence, from O stars above 30,000 K to M stars below 3,700 K. Each class is subdivided 0 to 9 from hotter to cooler. The Sun is G2V, placing it in the cooler half of the G class at 5,772 K. A star classified G5 is cooler than G2; a star classified G0 is hotter.

Why do hotter stars appear blue and cooler stars appear red?

Wien's displacement law states that peak emission wavelength is inversely proportional to temperature. A 30,000 K star peaks in the ultraviolet and emits strongly across all visible wavelengths with a blue surplus. A 3,000 K star peaks in the near-infrared and emits visible light only at the red end of the spectrum. The Wien's Law tab in the calculator lets you compute peak wavelength for any input temperature.

What is the hottest known star?

WR 102, a Wolf-Rayet star, has an estimated surface temperature of approximately 210,000 K, making it one of the hottest currently confirmed stars. Some central stars of planetary nebulae during their early white dwarf phase can briefly reach similar extremes. These objects are often too UV-bright to study with optical telescopes alone.

Can this calculator be used for brown dwarfs?

Yes. The Stefan-Boltzmann calculation works for any blackbody emitter, including brown dwarfs, which span roughly 300 to 2,100 K. At the coolest T and Y dwarf temperatures, molecular and dust opacity cause the actual spectrum to deviate substantially from an ideal blackbody, so the calculated temperature is a useful theoretical reference rather than a precise photospheric measurement.

What is the difference between effective temperature and core temperature?

Effective temperature describes the photosphere (the visible surface), ranging from about 2,400 K for the coolest M dwarfs to over 200,000 K for Wolf-Rayet stars. Core temperatures are orders of magnitude higher: roughly 15 million K for the Sun, up to 40 million K for massive main-sequence stars, and briefly reaching several billion K during the core collapse of supernovae. Nuclear fusion occurs only in the core; this calculator addresses photospheric temperature exclusively.