square metres per second (m2/s) to stokes (St) conversion

1 m2/s = 10000 StSt → m2/s
Formula
1 m2/s = 10000 St

Understanding Square Metres Per Second to Stokes Conversion

The square metre per second (m²/s) is the SI unit of kinematic viscosity, while the stokes (St) is the CGS unit equal to one square centimetre per second. Since one metre is a hundred centimetres, the areas differ by a factor of ten thousand. This conversion links modern SI fluid-dynamics work with classical CGS rheology literature, where viscosity is still frequently quoted in stokes.

Conversion Formula

1 m2/s=10000.0 St1\ \text{m2/s} = 10000.0\ \text{St}

To convert square metres per second to stokes, multiply by this factor:

St=m2/s×10000\text{St} = \text{m2/s} \times 10000

Step-by-Step Example

Convert 25 square metres per second to stokes.

St=25×10000=250000 St\text{St} = 25 \times 10000 = 250000\ \text{St}

How to Convert Square Metres Per Second to Stokes

Use this method to express an SI kinematic-viscosity value in CGS stokes.

  1. Note the factor: One square metre per second equals 10,000 stokes.
  2. Take your value: Record the kinematic viscosity in m²/s.
  3. Multiply: Multiply by 10,000 to obtain stokes.
  4. Worked result: For 25 m²/s, 25 × 10,000 = 250,000 St.

square metres per second to stokes conversion table

square metres per second (m2/s)stokes (St)
00
110000
220000
330000
440000
550000
660000
770000
880000
990000
10100000
15150000
20200000
25250000
30300000
40400000
50500000
60600000
70700000
80800000
90900000
1001000000
1501500000
2002000000
2502500000
3003000000
4004000000
5005000000
6006000000
7007000000
8008000000
9009000000
100010000000
200020000000
300030000000
400040000000
500050000000
10000100000000
25000250000000
50000500000000
1000001000000000
2500002500000000
5000005000000000
100000010000000000

What is the square metre per second?

The square metre per second (m²/s) is the SI derived unit of kinematic viscosity and of diffusivity. Kinematic viscosity is the ratio of a fluid's dynamic viscosity to its density, describing how readily a fluid flows under gravity independent of its mass.

Definition

One square metre per second is the SI coherent unit of kinematic viscosity, obtained by dividing dynamic viscosity (Pa·s) by density (kg/m³):

1 m2/s=1 m2/s1\ \text{m}^2/\text{s} = 1\ \text{m}^2/\text{s}

Equivalently, 1 m2/s=1 Pa·s÷1 kg/m31\ \text{m}^2/\text{s} = 1\ \text{Pa·s} \div 1\ \text{kg/m}^3. Its dimensions are area per time (L²T⁻¹). The same unit measures mass diffusivity and thermal diffusivity.

Origin and History

The concept of kinematic viscosity was developed in fluid mechanics to separate a fluid's resistance to shear (dynamic viscosity) from the inertial effect of its density. The SI adopted the coherent unit m²/s as part of the metre-kilogram-second framework, replacing the older CGS stokes (cm²/s).

Law and Notable Facts

The m²/s is the SI-preferred unit, but it is inconveniently large for most liquids, so the millimetre-squared per second (mm²/s), equal to the centistokes, dominates practical tabulation. The Reynolds number, Re=vL/νRe = vL/\nu, uses kinematic viscosity ν\nu directly in m²/s.

Real-World Examples and Conversions

Water at 20 °C has a kinematic viscosity of about 1.004×10−6 m2/s1.004\times10^{-6}\ \text{m}^2/\text{s} (1.004 cSt). Air at 20 °C is roughly 1.5×10−5 m2/s1.5\times10^{-5}\ \text{m}^2/\text{s}, higher than water because of air's low density. One m2/s\text{m}^2/\text{s} equals 10,000 stokes10{,}000\ \text{stokes} or 106 mm2/s10⁶\ \text{mm}^2/\text{s}.

What is the stokes?

The stokes (St) is the CGS unit of kinematic viscosity, equal to one square centimetre per second. Its common submultiple, the centistokes (cSt), is the everyday unit for reporting the kinematic viscosity of oils and other liquids.

Definition

One stokes equals one square centimetre per second, which in SI units is:

1 St=0.0001 m2/s1\ \text{St} = 0.0001\ \text{m}^2/\text{s}

Because 1 cm=10−2 m1\ \text{cm} = 10⁻²\ \text{m}, area scales as 10−410⁻⁴, so 1 St=1 cm2/s=10−4 m2/s1\ \text{St} = 1\ \text{cm}^2/\text{s} = 10⁻⁴\ \text{m}^2/\text{s} exactly. One hundredth of a stokes is a centistokes: 1 cSt=10−6 m2/s=1 mm2/s1\ \text{cSt} = 10⁻⁶\ \text{m}^2/\text{s} = 1\ \text{mm}^2/\text{s}.

Origin and History

The unit is named after the Irish-British mathematician and physicist Sir George Gabriel Stokes (1819–1903), whose work on fluid dynamics includes Stokes' law for the drag on a sphere and the Navier–Stokes equations. It was introduced as the natural CGS unit for kinematic viscosity, paralleling the poise for dynamic viscosity.

Law and Notable Facts

The stokes is a CGS unit and is not part of SI, which uses m²/s. Kinematic viscosity in stokes equals dynamic viscosity in poise divided by density in g/cm³ — a clean relationship within the CGS system, since water's density is very close to 1 g/cm³.

Real-World Examples and Conversions

Water at 20 °C has a kinematic viscosity of about 0.01 St, i.e. roughly 1 cSt. One stokes (10−4 m2/s10⁻⁴\ \text{m}^2/\text{s}, or 100 cSt) is comparable to a moderately heavy oil. To convert, 1 St=100 cSt=100 mm2/s1\ \text{St} = 100\ \text{cSt} = 100\ \text{mm}^2/\text{s}, and 1 m2/s=10,000 St1\ \text{m}^2/\text{s} = 10{,}000\ \text{St}.

Frequently Asked Questions

How many stokes are in one square metre per second?

One square metre per second equals 10,000 stokes, because a square metre is 10,000 square centimetres and the stokes is one square centimetre per second.

What formula converts m²/s to stokes?

Multiply the m²/s value by 10,000. For example, 0.5 m²/s equals 5,000 St.

How does the stokes relate to the centistokes?

One stokes equals 100 centistokes, so 1 m²/s is 10,000 St or 1,000,000 cSt — the same quantity expressed at different scales.

Where is this conversion useful?

It helps interpret older CGS-based viscosity measurements and rheology papers in terms of SI values used in modern simulation and engineering.

How do I convert stokes back to m²/s?

Divide the stokes value by 10,000, or multiply by 0.0001, so 2,500 St equals 0.25 m²/s.

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Complete square metres per second conversion table

m2/s
UnitResult
square millimetres per second (mm2/s)1000000 mm2/s
stokes (St)10000 St
centistokes (cSt)1000000 cSt
square feet per second (ft2/s)10.76391 ft2/s

Kinematic viscosity conversions