Local gravity estimate
Estimate local gravity from latitude with the GRS80 normal gravity formula. It is an estimate: normal gravity on the ellipsoid, not corrected for your site’s height or geology. For calibration work use a surveyed g, or a predicted one from NOAA NGS (US) or PTB SIS, and enter it in the deadweight tester calculator instead.
Local gravity estimate · GRS80
v0.1.0 · Moritz GRS80Estimate only: GRS80 normal gravity on the ellipsoid (height 0). Real gravity at a site differs from it because of height and local geology.
Not corrected for height: g falls as you go up, so for a lab above sea level this estimate is high. The free-air correction is not included until its source can be verified.
For calibration work use a surveyed value, or a predicted one: NOAA NGS Surface Gravity Prediction (US) or the PTB Gravity Information System (SIS). Enter it as g; it takes precedence.
Test vectors for this tool
The reference cases this calculator is tested against on every change. Use them to check your own software. All test vectors · Download JSON
| ID | Inputs | Expected | Tolerance | Source |
|---|---|---|---|---|
| GRAV-01 | latitude = 0 | 9.7803267715 m/s² | ± 1e-12 | H. Moritz, Geodetic Reference System 1980, The Geodesist’s Handbook, J. Geodesy 74 (2000) 128–133, section 4 (printed value). |
| GRAV-02 | latitude = 90 | 9.8321863685 m/s² | ± 1e-10 | H. Moritz, Geodetic Reference System 1980, The Geodesist’s Handbook, J. Geodesy 74 (2000) 128–133, section 4 (printed value). |
| GRAV-03 | latitude = 45 | 9.806199203 m/s² | ± 1e-9 | H. Moritz, Geodetic Reference System 1980, The Geodesist’s Handbook, J. Geodesy 74 (2000) 128–133, section 4 (printed value). |
| GRAV-04 | latitude = 41.3 | 9.802860530015392 m/s² | ± 1e-12 | Hand-derived with mpmath (50 digits) from the GRS80 closed formula γ = γₑ(1 + k sin²φ)/√(1 − e² sin²φ), constants from Moritz (2000) section 4. |
| GRAV-05 | latitude = -45 | 9.8061992024865 m/s² | ± 1e-12 | Hand-derived with mpmath (50 digits) from the GRS80 closed formula γ = γₑ(1 + k sin²φ)/√(1 − e² sin²φ), constants from Moritz (2000) section 4. |
| GRAV-06 | latitude = 90.5 | OutOfRangeError per rule | exact | Metrology Bench rule: refuse rather than extrapolate |
| GRAV-07 | g = 32.174 | OutOfRangeError per rule | exact | Metrology Bench rule: refuse rather than extrapolate |
| GRAV-08 | g = 9.80123, latitude = 45 | 9.80123 m/s² | ± 0 | Metrology Bench rule: a user-entered g takes precedence over the estimate. |
Put this calculator on your site
Free for labs, schools and anyone else. Paste this into your page.
<iframe src="https://metrologybench.com/embed/local-gravity" title="Local gravity estimate · Metrology Bench" width="100%" height="700" style="border:0;max-width:640px" loading="lazy"></iframe>
Ask your AI
Connect metrology-toolbox-mcp and your assistant runs this exact calculation, with the source in the answer.