square metres per second (m2/s) to square millimetres per second (mm2/s) conversion

1 m2/s = 1000000 mm2/smm2/s → m2/s
Formula
1 m2/s = 1000000 mm2/s

Understanding Square Metres Per Second to Square Millimetres Per Second Conversion

The square metre per second (m²/s) is the SI unit of kinematic viscosity, and the square millimetre per second (mm²/s) is a smaller metric unit that is numerically identical to the centistokes. Because a millimetre is one thousandth of a metre, the areas differ by a factor of a million. This conversion is common when reporting fluid data on lubricant and fuel datasheets, where mm²/s is the SI-consistent stand-in for the familiar centistokes.

Conversion Formula

1 m2/s=1.00000×106 mm2/s1\ \text{m2/s} = 1.00000 \times 10⁶\ \text{mm2/s}

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

mm2/s=m2/s×1000000\text{mm2/s} = \text{m2/s} \times 1000000

Step-by-Step Example

Convert 25 square metres per second to square millimetres per second.

mm2/s=25×1000000=25000000 mm2/s\text{mm2/s} = 25 \times 1000000 = 25000000\ \text{mm2/s}

How to Convert Square Metres Per Second to Square Millimetres Per Second

Follow these steps to scale an SI kinematic-viscosity value down to square millimetres per second.

  1. Know the factor: One square metre per second equals 1,000,000 square millimetres per second.
  2. Record your value: Take the kinematic viscosity in m²/s.
  3. Multiply by one million: Multiply by 1,000,000 to reach mm²/s (equivalently centistokes).
  4. Worked result: For 25 m²/s, 25 × 1,000,000 = 25,000,000 mm²/s.

square metres per second to square millimetres per second conversion table

square metres per second (m2/s)square millimetres per second (mm2/s)
00
11000000
22000000
33000000
44000000
55000000
66000000
77000000
88000000
99000000
1010000000
1515000000
2020000000
2525000000
3030000000
4040000000
5050000000
6060000000
7070000000
8080000000
9090000000
100100000000
150150000000
200200000000
250250000000
300300000000
400400000000
500500000000
600600000000
700700000000
800800000000
900900000000
10001000000000
20002000000000
30003000000000
40004000000000
50005000000000
1000010000000000
2500025000000000
5000050000000000
100000100000000000
250000250000000000
500000500000000000
10000001000000000000

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 square millimetre per second?

The square millimetre per second (mm²/s) is the practical SI unit of kinematic viscosity, numerically identical to the centistokes (cSt). It is the unit in which most liquid viscosities are quoted in engineering and lubrication data sheets.

Definition

One square millimetre per second is one millionth of a square metre per second:

1 mm2/s=0.000001 m2/s1\ \text{mm}^2/\text{s} = 0.000001\ \text{m}^2/\text{s}

Because 1 mm=10−3 m1\ \text{mm} = 10⁻³\ \text{m}, area scales as 10−610⁻⁶, so 1 mm2/s=10−6 m2/s1\ \text{mm}^2/\text{s} = 10⁻⁶\ \text{m}^2/\text{s}. It is exactly equal to one centistokes: 1 mm2/s=1 cSt1\ \text{mm}^2/\text{s} = 1\ \text{cSt}.

Origin and History

As the SI displaced the CGS system, the centistokes was re-expressed in coherent SI form as mm²/s, keeping the numerical values in existing tables unchanged. This convenient one-to-one equality made the transition seamless for industries such as petroleum and lubricants that had decades of data in centistokes.

Law and Notable Facts

It is a coherent submultiple within SI usage and the de facto standard for viscosity grades. ISO viscosity grade (VG) numbers, such as ISO VG 46, are defined by the fluid's mid-point kinematic viscosity in mm²/s at 40 °C — so ISO VG 46 oil is nominally 46 mm²/s at 40 °C.

Real-World Examples and Conversions

Water at 20 °C is about 1.004 mm²/s (1.004 cSt). Typical engine oil at 100 °C ranges from roughly 5 to 21 mm²/s depending on SAE grade. One mm2/s\text{mm}^2/\text{s} equals 10−6 m2/s10⁻⁶\ \text{m}^2/\text{s} and 10−2 stokes10⁻²\ \text{stokes}.

Frequently Asked Questions

How many square millimetres per second are in one square metre per second?

There are exactly 1,000,000 square millimetres per second in one square metre per second, because one square metre contains a million square millimetres.

Is mm²/s the same as centistokes?

Yes, one square millimetre per second is numerically equal to one centistokes, so datasheets often use the two interchangeably.

What is the multiplication rule?

Multiply the m²/s value by one million to obtain mm²/s. For example, 0.0004 m²/s equals 400 mm²/s.

Why convert to mm²/s at all?

Real fluids have very small kinematic viscosities in m²/s, so mm²/s (equivalently cSt) keeps figures like a 46-grade hydraulic oil at a readable 46 mm²/s rather than 0.000046 m²/s.

How is the reverse conversion done?

Divide the mm²/s value by 1,000,000, or multiply by 1 × 10⁻⁶, so 250 mm²/s equals 0.00025 m²/s.

People also convert

m2/s to Stm2/s to cStm2/s to ft2/s

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