# Common conversion factors for water, ice, sea-level & air

Pure (fresh) liquid water has a density of about 1.000 kg/liter, or equivalently 1.000 g/cm3, or 1000 kg/m3 (1.000 metric tonnes), at 4.3°C and 1 atm pressure.

The units are often omitted, so the density of liquid H2O may be stated as simply 1.000

Ice has a density of about 0.9167

Seawater has a density of about 1.027

The Dead Sea is nearly 10x as salty as the ocean, and has a density of about 1.240

The density of water varies only slightly with temperature & pressure, but if you need more precision various online tables and calculators can give you nearly exact water densities for specific temperatures, pressures & salinities.

1 km = 0.621371 mile,
so 1 km3 (cubic kilometer, or cu-km) = 0.239913 mi3

```1 GT = 1 gigaton = one billion tons
= 109 tons (U.S. tons or "short tons," each 907.185 kg or 2000 lbs)

1 Gt = 1 gigatonne
= 1 Pg = 1 petagram = 1015 grams
= 1000 Tg = 1000 teragrams
= 109 tonnes (metric tons, each 1000 kg or 2204.62 lbs)
= 1012 kg
= 1.1023 GT
= the mass of 1 cubic kilometer of fresh water
= the mass of 1.091 cubic km of ice
= the mass of 0.240 cubic miles of fresh water
= the mass of 0.262 cubic miles of ice

1 cubic mile of ice weighs 1/0.262 = 3.82 Gt
```

The Earth's atmosphere is variously estimated to have a mass of 5.1 to 5.3 × 1018 kg = 5.3 × 106 Gt = 5.3 million Gt, so (using the “5.3” estimate) one ppmm (part-per-million by mass) weighs about 5.3 Gt.

However, atmospheric gas concentrations are customarily expressed in ppmv (parts-per-million by volume, a/k/a molar fraction, µ mol/mol), so to calculate the mass of one ppmv requires scaling according to the molecular weight of the gas in question. (Note: if water vapor is ignored this is properly called the dry molar fraction.)

The average molecular weight of the Earth's atmosphere is 28.966 g/mole (~29). So, for example:

Carbon Dioxide:
1 ppmv CO2 (molecular wt 44.01) has mass ~(44/29) × 5.3 Gt = 8.053 Gt, of which 12/44-ths or 2.196 Gt is carbon.
1 Pg = 1 Gt, so 1 PgC (“petagrams carbon”) is contained in (44/12) = 3.667 Gt CO2, and is equivalent to 3.667/8.053 = 0.4553 ppmv CO2 in the atmosphere.
408 ppmv CO2 has mass 408 × 8.053 Gt/ppmv = 3286 Gt.
That much CO2 contains (12/44)×3286 = 896 PgC.

Methane:
1 ppmv CH4 (molecular wt 16.044) has mass ~(16/29) × 5.3 Gt = 2.9356 Gt.
1.85 ppmv CH4 has mass 1.85 × 2.9356 Gt/ppmv = 5.431 Gt.

Meltwater & sea-level:
The oceans cover about 3.618 × 108 km2 (sq-km) = 3.618 × 1014 m2. A one mm global average increase in sea-level requires 1/1000-th of a cubic meter of water for each square meter of ocean surface: 10-3 m3 × (3.618 × 1014) = 3.618 × 1011 m3 of water.
(Note: sea ice is frozen nearly-fresh water, not saltwater, because most of the salt is expelled when seawater freezes.)
A cubic meter of fresh water weighs 1000 kg, so (disregarding the minor salinity/density effects of mixing fresh meltwater with seawater) a one mm increase in sea-level requires about 3.618 × 1014 kg = 361.8 Gt of meltwater.
Ice has a density of about 0.9167, so 361.8 Gt = ~394.7 km3, which is 94.7 cubic miles.
Calculated another way, 361.8 Gt/mm-SLR × 0.262 mi3/Gt = 94.8 cubic miles per millimeter of sea-level rise.
Melting ~95 cubic miles of grounded ice (= 362 Gt = 395 km3) into ~87 cubic miles of fresh water and adding it to the oceans would raise globally averaged sea-level by 1 mm.

-Dave Burton  3/28/2014, 8/18/2014, 5/10/2015, 12/9/2015, 12/13/2016, 2/3/2017, 6/25/2018, 12/23/2018

which are the approximate current average atmospheric concentrations of the two gasses: 408 ppmv CO2 and 1.85 ppmv CH4

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