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

1 St = 0.0001 m2/sm2/s → St
Formula
1 St = 0.0001 m2/s

Understanding stokes to square metres per second Conversion

The stokes (St) is the CGS unit of kinematic viscosity, equal to one square centimetre per second, while the square metre per second (m2/s) is the coherent SI unit of the same quantity. Since one metre contains 100 centimetres, an area ratio of 10,000 links the two, making the stokes a small fraction of an SI unit. This conversion is essential when feeding legacy viscosity data into modern SI-based fluid-dynamics calculations.

Conversion Formula

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

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

m2/s=St×0.0001\text{m2/s} = \text{St} \times 0.0001

Step-by-Step Example

Convert 25 stokes to square metres per second.

m2/s=25×0.0001=0.0025 m2/s\text{m2/s} = 25 \times 0.0001 = 0.0025\ \text{m2/s}

How to Convert stokes to square metres per second

Bringing CGS kinematic viscosity into SI units requires just one multiplication by a power of ten.

  1. Record the stokes value: Take your viscosity measurement in St.
  2. Multiply by 0.0001: This is the exact number of m2/s in one stokes.
  3. Report in SI: The result is your viscosity in m2/s, ready for SI calculations.
  4. Worked result: 25 St × 0.0001 = 0.0025 m2/s.

stokes to square metres per second conversion table

stokes (St)square metres per second (m2/s)
00
10.0001
20.0002
30.0003
40.0004
50.0005
60.0006
70.0007
80.0008
90.0009
100.001
150.0015
200.002
250.0025
300.003
400.004
500.005
600.006
700.007
800.008
900.009
1000.01
1500.015
2000.02
2500.025
3000.03
4000.04
5000.05
6000.06
7000.07
8000.08
9000.09
10000.1
20000.2
30000.3
40000.4
50000.5
100001
250002.5
500005
10000010
25000025
50000050
1000000100

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}.

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}.

Frequently Asked Questions

How many square metres per second are in one stokes?

One stokes equals exactly 0.0001 m2/s, which is one ten-thousandth of an SI unit. This clean factor comes from the 100:1 ratio between metres and centimetres, squared.

Why is the SI unit so much larger than the stokes?

Because the m2/s is based on the metre while the stokes is based on the centimetre, and squaring the 100-fold length ratio gives a 10,000-fold area ratio. As a result m2/s values are numerically tiny for common fluids.

How do I convert square metres per second back to stokes?

Multiply the m2/s value by 10,000. For instance, 1 m2/s equals 10,000 St.

Which unit do scientific papers prefer?

Modern SI-based literature reports kinematic viscosity in m2/s, though centistokes remains common in industry for readability.

What is 25 stokes in m2/s?

It is 0.0025 m2/s, obtained by multiplying 25 by 0.0001.

People also convert

St to mm2/sSt to cStSt to ft2/s

Complete stokes conversion table

St
UnitResult
square metres per second (m2/s)0.0001 m2/s
square millimetres per second (mm2/s)100 mm2/s
centistokes (cSt)100 cSt
square feet per second (ft2/s)0.001076391 ft2/s

Kinematic viscosity conversions