Standard gravity, 9.80665 m/s², is a fixed reference value for the acceleration of a falling body near the Earth's surface. We ran the reference formula for Earth's gravity, with sea level taken as the GRS 80 ellipsoid, and it puts sea-level normal gravity at 9.78035 m/s² in Singapore, 9.78048 in Kuala Lumpur and 9.78093 in Jakarta. All three are 0.26–0.27% below standard gravity. On the same formula, 9.80665 is reached only at about 45.5° latitude, north or south. The number itself is a convention: the 3rd General Conference on Weights and Measures adopted it by declaration in 1901, as a value "already stated in the laws of some countries", and the declaration names no place or latitude for it.
A 1901 declaration adopted standard gravity without a bearing
The BIPM publishes the text as Declaration 2 of the 3rd CGPM (1901), from page 70 of the proceedings. It sets the "standard acceleration due to gravity" at 980.665 cm/s² and defines the standard weight of a body as its mass times that acceleration. The BIPM adds that it was the reference for the now obsolete kilogram-force.
NIST lists the standard acceleration of gravity among the 2022 CODATA recommended values as 9.806 65 m s⁻², and gives its uncertainty as exact. The declaration offers no derivation, and the nineteenth-century records behind secondary accounts of its origin were not ones we could open, so we leave that story out.
The reference formula charts g at every latitude
Geodesists describe gravity on a smooth model Earth with a closed formula usually given Somigliana's name. H. Moritz's account of the Geodetic Reference System 1980, in the Journal of Geodesy, says the theory of the equipotential ellipsoid behind it was first given by Pizzetti in 1894 and further elaborated by Somigliana in 1929. The closed form, as the National Imagery and Mapping Agency printed it for WGS 84 in its 1999 note Gravity Station Data Format & Anomaly Computations, is γ = γe (1 + k sin²φ) / √(1 − e² sin²φ), where φ is geodetic latitude.
We used the GRS 80 constants Moritz gives: γe = 9.7803267715 m/s² at the equator, k = 0.001931851353 and e² = 0.00669438002290. Before trusting our script, we checked it against his published values.
| Check | Our result | Published |
|---|---|---|
| Normal gravity at the pole | 9.8321863685 | 9.8321863685 (Moritz) |
| Normal gravity at 45° | 9.806199202 | 9.806199203 (Moritz) |
| Closed formula against Moritz's series, 901 latitudes | within 1.5 × 10⁻¹⁰ m/s² | series stated to 10⁻¹⁰ relative |
| GRS 80 against WGS 84, all latitudes | within 1.44 × 10⁻⁶ m/s² | WGS 84 constants (NIMA 1999) |
City latitudes are approximate centre values; an error of 0.1° moves the result by under 1 × 10⁻⁴ m/s². The newton column is our arithmetic.
| City | Latitude | Normal gravity at sea level (m/s²) | Against 9.80665 | Weight of 70 kg with normal gravity (N) |
|---|---|---|---|---|
| Singapore | 1.29° N | 9.78035 | −0.268% | 684.62 |
| Kuala Lumpur | 3.15° N | 9.78048 | −0.267% | 684.63 |
| Jakarta | 6.21° S | 9.78093 | −0.262% | 684.67 |
| Manila | 14.60° N | 9.78361 | −0.235% | 684.85 |
| Hong Kong | 22.30° N | 9.78777 | −0.193% | 685.14 |
| Taipei | 25.03° N | 9.78958 | −0.174% | 685.27 |
| Tokyo | 35.68° N | 9.79792 | −0.089% | 685.85 |
| Oslo | 59.91° N | 9.81911 | +0.127% | 687.34 |
Today's chart plots standard gravity at about 45.5°
Solving the formula for 9.80665 gives a latitude of 45.50°. That is our own computation on GRS 80; we found no published figure for it and offer no reason for it. Moritz gives normal gravity at exactly 45° as 9.806199203 m/s², which sits 45 mGal (4.5 × 10⁻⁴ m/s²) below the declared value.
The two common roundings land elsewhere. On our runs, sea-level normal gravity reaches 9.8 at 38.08° and 9.81 at 49.21°. No place in the table from Singapore to Tokyo reaches even 9.80 at sea level. Oslo comes out 0.40% above Singapore.
Each metre up logs about 0.31 mGal less on the chart
The NIMA note also gives the vertical gradient of normal gravity, citing Heiskanen and Moritz's Physical Geodesy (1967). At Singapore's latitude the first-order gradient works out to 0.3088 mGal per metre, about one part in 3.17 million of g for every metre of height. These are free-air figures above the ellipsoid.
By our arithmetic, 100 m of height takes 0.003% off normal gravity and 1,000 m takes 0.032%. At 8,849 m the formula gives 9.75309 m/s², 0.279% below its sea-level value. Matching the Singapore–Oslo difference by height alone would take about 12.6 km of free air. A real mountain adds the attraction of its own rock (the Bouguer term in the NIMA note), so gravity on a summit falls by less; we did not compute that term.
Latitude takes a PE figure further off course than syllabus rounding
Potential energy is mgh, so any change in g passes straight through to the answer. Raise 70 kg through 10 m and, by our arithmetic, standard gravity gives 6,864.655 J, and Singapore's sea-level normal gravity gives 6,846.247 J. The standard-gravity figure is 0.27% above the normal-gravity one. Switching between 9.8 and 9.81 moves the answer by 0.10%, so the change of place weighs more than twice as much. Rounding g to 10 moves it by about 2%. The Cambridge IGCSE Physics 0625 syllabus for 2026–2028 asks candidates to state that g near the Earth's surface is approximately 9.8 m/s².
Our potential energy calculator can show this. Until a fix dated 6 November 2026, it told readers it used g = 9.81 while it computed with 9.80665, and its own worked example of 196 J could not be reproduced: typing 2.0 kg and 10 m printed 200 J. The revised version computes with 9.80665 by default and says so. Its Value of g menu also offers 9.81, 9.8, 10, a value of your own, and normal gravity at a chosen latitude and height. Enter 70 for mass and 10 for height, leave energy blank, choose normal gravity at a latitude under Value of g and pick Singapore as the city: it shows 6846.2 J, with 6846.24706 before rounding and −0.268% against standard gravity. Its height box for normal gravity takes −500 to 10,000 m, so the 12.6 km above is out of its range.
Only a gravimeter maps the rock beneath a city
Normal gravity is a reference model of the Earth. Gravity at one spot differs from it by a local anomaly, which comes from the rock below and the terrain around, and it also rises and falls slightly with the tides. We found no absolute gravity value we could open for Singapore, Kuala Lumpur, Jakarta or Manila, so the figures above stay model figures. Nor is mean sea level quite the ellipsoid; the gap, the geoid height, varies by place, and we did not look it up.
The broad pattern, low at the equator and high at the poles, comes from the Earth's spin and its flattened shape. Our guide to the gravitational constant G works through how much each contributes. The formula has no term for the hill a surveyor stands on, the basin under a city or the tide that afternoon. Those show up only when someone sets a gravimeter on the ground and reads it.
View author profile → · Editorial policy
