Standard acceleration of gravity

g_{n} = 9.80665\ \text{m/s}^{2}

Value	9.80665 m/s²
Status	Exact by definition — no uncertainty
Source	CGPM, 3rd meeting (1901); SI Brochure, 9th edition
Categories	Universal & Atomic Engineering & Trade

Standard acceleration of gravity in every acceleration unit

microgal	980,665,000 μGal
milligal	980,665 mGal
millimeter per second squared	9,806.65 mm/s²
centimeter per second squared	980.665 cm/s²
gal	980.665 Gal
inch per second squared	386.08858 in/s²
kilometer per hour per second	35.30394 km/h/s
foot per second squared	32.174049 ft/s²
mile per hour per second	21.936851 mph/s
meter per second squared	9.80665 m/s²
standard gravity	1 g

Learning zone

The 3rd CGPM adopted 9.806 65 m/s² in 1901 as a conventional standard, originally tied to sea level at 45° latitude. It is exact by agreement, which is what makes the kilogram-force, the pound-force, the psi-to-head conversion and the "g" of acceleration well-defined units rather than fuzzy ones. Aviation, structural codes and instrument calibration all quote it.

Actual gravity is not 9.806 65 anywhere in particular. Earth's rotation and equatorial bulge give about 9.780 m/s² at the equator and 9.832 m/s² at the poles — a 0.5 % spread — and altitude removes a further 3 × 10⁻⁶ m/s² per metre of elevation, with local geology adding milligal wiggles that gravimetric surveys hunt for. Use g_n for defined units and legal metrology; use a measured local g when weighing to parts per million.

Used by 36 solvers

Acceleration Down a Frictionless Incline

a = g \sin\theta

Acceleration Down an Incline with Friction

a = g\left(\sin\theta - \mu_k \cos\theta\right)

Atwood Machine Acceleration

a = \frac{\left(m_1 - m_2\right) g}{m_1 + m_2}

Banked Curve Angle

\theta = \arctan\!\left(\frac{v^{2}}{r g}\right)

Bed Shear Stress in an Open Channel

\tau_0 = \rho \, g \, R \, S

Bernoulli's Equation (Two Points)

P_1 + \tfrac{1}{2}\rho v_1^{2} + \rho g z_1 = P_2 + \tfrac{1}{2}\rho v_2^{2} + \rho g z_2

Briggs Buoyancy Flux

F = \frac{g \, v_s \, d^2 (T_s - T_a)}{4 \, T_s}

Buoyant Force (Archimedes' Principle)

F_b = \rho V g

Conservation of Mechanical Energy (½mv² + mgh)

\tfrac{1}{2} v_1^{2} + g h_1 = \tfrac{1}{2} v_2^{2} + g h_2

Critical Shear Stress for Sediment Entrainment

\tau_c = \theta_c \, (s - 1) \, \rho \, g \, d

Cyclic Stress Ratio for Liquefaction

\mathrm{CSR} = 0.65\,\dfrac{a_{max}}{g}\,\dfrac{\sigma_v}{\sigma'_v}\,r_d

Darcy–Weisbach Head Loss

h_f = f \, \frac{L}{D} \, \frac{v^{2}}{2g}

Drop Height of a Horizontally Launched Projectile

y = \tfrac{1}{2} g t^{2}

Gravitational Field Strength

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

Gravitational Potential Energy (U = mgh)

U = m g h

Hydraulic Power (P = ρgQh)

P = \rho g Q h

Hydronic Static Fill Pressure

P = \rho_w g H + P_{margin}

Hydrostatic Pressure (P = ρgh)

P = \rho g h

Maximum Speed on a Flat Curve

v_{\max} = \sqrt{\mu_s g r}

Minor Loss from K Factor

h_L = K \, \frac{v^{2}}{2g}

Normal Force on an Incline (N = mg cos θ)

N = m g \cos\theta

Pressure Head (h = P/ρg)

h = \frac{P}{\rho g}

Projectile Maximum Height

H = \frac{v_0^{2} \sin^{2}\theta}{2g}

Projectile Range on Level Ground

R = \frac{v_0^{2} \sin 2\theta}{g}

Projectile Time of Flight

T = \frac{2 v_0 \sin\theta}{g}

Rope Tension When Lifting a Mass

T = m\left(g + a\right)

Shields Parameter (Dimensionless Shear Stress)

\theta = \frac{\tau}{(\rho_s - \rho) \, g \, d}

Simple Pendulum Period

T = 2\pi \sqrt{\frac{L}{g}}

Stack Draft Pressure (Chimney Effect)

\Delta p = h \, g \, (\rho_a - \rho_s)

Stokes Settling Velocity

v_s = \frac{g (\rho_s - \rho) d^2}{18 \mu}

Terminal Velocity

v_t = \sqrt{\frac{2 m g}{\rho A C_d}}

Torricelli's Law (v = √(2gh))

v = \sqrt{2 g h}

V-Notch (Triangular) Weir Flow

Q = \frac{8}{15} C_d \sqrt{2g} \, \tan\!\frac{\theta}{2} \, H^{5/2}

Velocity Head (h = v²/2g)

h_v = \frac{v^{2}}{2g}

Weight (W = mg)

W = m g

Weight Component Along an Incline (mg sin θ)

F_{\parallel} = m g \sin\theta