Stellar Surface Gravity / log g Calculator

Calculate a star's surface gravity g = GM/R² from its mass and radius, and the astronomically standard log g (base-10 log of g in cgs units), with a rough dwarf/giant/supergiant/white-dwarf/neutron-star classification, a log g ladder, and a mass-radius diagram with constant-log-g contour lines.

Surface gravity / log g calculator

Surface gravity g = GM/R² is almost always quoted as log g — the base-10 logarithm of g in cgs units (cm/s²) — because it spans such a huge range across stellar types. The Sun: g ≈ 2.74 × 10⁴ cm/s², log g ≈ 4.44. Giants and supergiants have enormous radii and correspondingly tiny log g; compact remnants (white dwarfs, neutron stars) have minuscule radii and enormous log g.

Mass (M)

Radius (R)

log g ≈ +4.44Dwarf (main sequence)

g = 27397.2 cm/s² = 274 m/s² · 27.937× Earth's surface gravity

Supergiant → giant → dwarf → white dwarf → neutron star, left to right — a rough guide, not a substitute for spectroscopic luminosity classification.

Diagonal lines mark constant log g (each has slope ½ in this log-log space, since g ∝ M/R²). Where a star sits relative to them is its log g, read directly off the chart.

Ask how strong gravity is at a star’s surface, and the honest answer depends entirely on how much the star has puffed up or collapsed — mass alone tells you surprisingly little. A red giant can outweigh the Sun and still have gravity dozens of times weaker at its surface, simply because its radius is enormous; a white dwarf with the Sun’s mass crammed into Earth’s size has surface gravity hundreds of thousands of times stronger. Surface gravity, more than mass, is what tells you what kind of star you’re looking at.

The formula, and why log g

g = \frac{GM}{R^2}

Straightforward — but astronomers almost never quote g directly. Instead, by long-standing convention, g is computed in cgs units (centimeters and grams, not meters and kilograms) and then log₁₀’d, giving log g. The Sun: g ≈ 2.74 × 10⁴ cm/s², log g ≈ 4.44 — a number worth memorizing, since virtually every other log g gets compared against it implicitly.

The reason for the logarithm is the same reason magnitude and pH use one: the actual range of g across real stars spans roughly 20 orders of magnitude, from bloated red supergiants to neutron stars. A single logarithmic number makes that entire range comparable at a glance.

What log g tells you

log g ≈ 3.5–4.6 (dwarf / main sequence): ordinary hydrogen-fusing stars across most of the mass range, the Sun included — mass and radius both scale up together along the main sequence, keeping log g in a comparatively narrow band.
log g ≈ 0.5–3 (giant): the star has expanded well beyond its main-sequence size (helium-burning red giants, for instance), which drives g down even though mass hasn’t changed much.
log g ≲ 0.5 (supergiant): an even more extreme radius — a red supergiant like Betelgeuse has a radius large enough that its surface gravity is less than Earth’s, despite the star having some 15+ times the Sun’s mass.
log g ≈ 6–9 (white dwarf): roughly a solar mass compressed into a radius similar to Earth’s — surface gravity in the hundreds of thousands of g.
log g ≳ 9 (neutron star): a solar-mass-plus object compressed to a radius of about 10 km. Surface gravity here reaches roughly 10¹⁴ times Earth’s — strong enough that “surface” itself starts to strain the everyday meaning of the word.

These bands are a genuinely useful rule of thumb, not a substitute for actual spectroscopic luminosity classification — real log g measurements (from pressure-broadened spectral lines, among other methods) are one of the standard tools used to determine that classification in the first place.

Reading the two charts

The log g ladder places every preset on one fixed scale from −1 to 15, colored by the same rough bands described above — seeing a red supergiant and a neutron star on the same axis, 14+ orders of magnitude apart, does more to convey the range than the numbers alone.
The mass-radius diagram plots (M, R) in log-log space with several dashed lines of constant log g overlaid. Because g ∝ M/R² exactly, every constant-log g line has the same slope (½) in this space — so a star’s log g is literally its position relative to those lines, the same logic behind the mass-luminosity charts elsewhere on this site.