1
R☉
0.16
6
1,783
0
dex
3.7618
dex
1
L☉
1
x
1
R☉
0.16
6
1,783
0
dex
3.7618
dex
1
L☉
1
x
The Hertzsprung-Russell (H-R) Diagram Calculator helps you locate a star on the most important diagram in stellar astrophysics and identify its physical properties. The H-R diagram, developed independently by Ejnar Hertzsprung and Henry Norris Russell in the early twentieth century, plots stellar luminosity against surface temperature and reveals the underlying order of stellar diversity.
When thousands of stars are plotted on the H-R diagram, they do not scatter randomly — they cluster into distinct groups. The main sequence is a diagonal band running from hot, luminous blue stars in the upper left to cool, dim red stars in the lower right. About 90% of all stars, including the Sun, lie on the main sequence. They are burning hydrogen in their cores and are in hydrostatic equilibrium.
Above and to the right of the main sequence lie the giant and supergiant branches — evolved stars that have expanded enormously after exhausting their core hydrogen. These stars can be hundreds or thousands of times more luminous than main sequence stars of similar temperature, purely because of their larger surface area. Red giants like Arcturus and Aldebaran, and supergiants like Betelgeuse and Rigel, populate this region.
Below and to the left lie the white dwarfs — the burned-out remnants of low and medium mass stars. Small, hot, and faint, white dwarfs radiate residual thermal energy and slowly cool over billions of years. They represent the ultimate fate of stars like our Sun.
This calculator uses the entered temperature and luminosity to compute the estimated radius via the Stefan-Boltzmann law, assign a spectral class, and identify the likely H-R diagram region. The B-V color index provides a color classification connecting the spectral analysis to photometric observations.
Radius from Stefan-Boltzmann (solar units): R = sqrt(L) x (T_sun/T)^2. Spectral class from temperature: O (>30,000 K), B (10,000-30,000 K), A (7,500-10,000 K), F (6,000-7,500 K), G (5,200-6,000 K), K (3,700-5,200 K), M (<3,700 K). H-R region identified by the combination of luminosity and temperature thresholds. B-V color index interpolated from the standard temperature-color calibration.
H-R region 0 = Supergiant/Giant (high luminosity, high temp), region 1 = Red Giant (high luminosity, low temp), region 2 = White Dwarf (low luminosity), region 3 = Hot massive main sequence (O/B), region 4 = Main Sequence. Radius significantly larger than expected from a main sequence star of the same temperature indicates an evolved (giant or supergiant) star.
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Rigel is a B-type supergiant. Its high luminosity and temperature place it firmly in the supergiant region of the H-R diagram, with a radius about 79 times the Sun's.
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Proxima Centauri, our nearest stellar neighbor, is an M-class red dwarf with temperature ~3,042 K and luminosity just 0.15% of the Sun's — placing it at the bottom of the main sequence.
The main sequence is a continuous band of stars on the H-R diagram that are burning hydrogen in their cores via nuclear fusion. It spans from massive, hot, blue O-type stars (upper left) to lightweight, cool, red M-type stars (lower right). The position of a star on the main sequence is determined almost entirely by its mass.
When a star exhausts the hydrogen in its core, nuclear burning ceases and the core contracts. The gravitational energy released heats the surrounding hydrogen shell, igniting shell burning, which causes the outer envelope to expand dramatically. The star moves off the main sequence to the right on the H-R diagram, becoming a giant or supergiant.
The Harvard classification system assigns spectral types O, B, A, F, G, K, M based primarily on surface temperature, running from hottest (O, >30,000 K) to coolest (M, <3,700 K). Each class is subdivided 0-9. The Sun is G2. The mnemonic is: Oh Be A Fine Girl/Guy Kiss Me. Modern additions include L, T, Y types for brown dwarfs.
The Morgan-Keenan (MK) system adds a luminosity class to the spectral type: I = supergiant, II = bright giant, III = giant, IV = subgiant, V = main sequence (dwarf). The Sun is G2V (G-type, subclass 2, main sequence). Rigel is B8Ia (B-type, supergiant). This two-dimensional classification encodes both temperature and evolutionary state.
White dwarfs appear in the lower left of the H-R diagram — they are hot but have very small radii (about the size of Earth), so their total luminosity is low despite their high temperature. As they cool over billions of years, they move to the right along the lower part of the diagram, eventually becoming theoretically cold black dwarfs (though none have had time to cool that far yet).
Horizontal branch stars are helium-burning stars in the cores of old globular clusters. After the red giant phase, when the helium ignites in a flash, stars settle into a horizontal band on the H-R diagram burning helium in their cores. The RR Lyrae variable stars lie on the instability strip crossing the horizontal branch and are important distance indicators.
The instability strip is a nearly vertical region on the H-R diagram where stars undergo pulsations — regular expansions and contractions. Cepheid variables and RR Lyrae variables lie in this strip. Their pulsation periods are related to their luminosities (the period-luminosity relation), making them crucial as standard candles for measuring cosmic distances.
Stellar evolution tracks — computed from models — trace paths on the H-R diagram showing how a star's position changes over time. A Sun-like star spends most of its life on the main sequence, then moves right and upward as it expands into a red giant, then drifts to the lower left as a hot white dwarf. The shape of these tracks depends sensitively on mass.
An isochrone (equal time) is a line on the H-R diagram connecting all points occupied by stars of the same age but different masses. Star clusters, in which all members formed at approximately the same time, trace out isochrones on the H-R diagram. The turn-off point — where stars leave the main sequence — moves to lower luminosity with age, providing a way to determine cluster ages.
It was the first diagram to reveal that stellar properties are not random but follow systematic patterns governed by physics. It provided the empirical basis for stellar astrophysics and served as a test bed for nuclear physics, quantum mechanics, and general relativity applied to stars. Every advance in stellar theory is ultimately tested against the H-R diagram.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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