Actually, everything depends on solvent you want to use  and temperature. If you want to know gyration (Rg) or hydrodynamic (Rh) radius, you should use one of the Kuhn–Mark–Houwink–Sakurada equations for dextran. MHS equation looks like Rg=a*(Mw)^b.  The coefficients a and b are sensitive to solvent and temperature.  

Another approach is to find a Kuhn segment length value for dextran in your solvent and calculate Rg based on Freely Jointed Chain (FJC).

Check these publications:

[1] Pavlov GM, Korneeva EV, Yevlampieva NP. Hydrodynamic characteristics and equilibrium rigidity of pullulan molecules. Int J Biol Macromol 1994;16:318–23.

[29]

[2]  Huber A. Characterization of branched and linear polysaccharides by size-exclusion chromatography/low-angle laser light scattering. J Appl Polym Sci Appl Polym Syrup 1991;48:95

[3] Cleland RL. Ionic polysaccharides. IV. Free-rotation dimensions for disaccharide polymers. Comparison with experiment for hyaluronic acid. Biopolymers 1970;9:811–824.

Actually, everything depends on solvent you want to use  and temperature. If you want to know gyration (Rg) or hydrodynamic (Rh) radius, you should use one of the Kuhn–Mark–Houwink–Sakurada equations for dextran. MHS equation looks like Rg=a*(Mw)^b.  The coefficients a and b are sensitive to solvent and temperature.  

Another approach is to find a Kuhn segment length value for dextran in your solvent and calculate Rg based on Freely Jointed Chain (FJC).

Check these publications:

[1] Pavlov GM, Korneeva EV, Yevlampieva NP. Hydrodynamic characteristics and equilibrium rigidity of pullulan molecules. Int J Biol Macromol 1994;16:318–23.

[29]

[2]  Huber A. Characterization of branched and linear polysaccharides by size-exclusion chromatography/low-angle laser light scattering. J Appl Polym Sci Appl Polym Syrup 1991;48:95

[3] Cleland RL. Ionic polysaccharides. IV. Free-rotation dimensions for disaccharide polymers. Comparison with experiment for hyaluronic acid. Biopolymers 1970;9:811–824.

As well as being able to measure hydrodynamic radius in the Zetasizer (if you have access to one), it's also provided with a calculator that allows size estimates from molecular mass and vice versa.  For more information, see the attached and:

http://www.materials-talks.com/blog/2014/09/16/faq-molecular-weight-estimate-from-dls/

If you have one or 2 calculations only then we can help you with these. There's obviously an assumption (or knowledge) of shape assumed (for example all in the same family as in Mark-Houwink) in all calculations of this type.

There is a formula that used to calculate the radius (in Angstrom) from the molar mass (in g/mol) of dextran,

a=0.33*(MM^0.46)

where, a and MM are radius and molar mass, respectively.

you can see this equation on attached paper.

Hi Alan F Rawle sir, Can you help me in calculating the size of dextran 6 (molecular weight= 6000) and dextran 70 (molecular weight 70000)

@ Nilimesh See attached.

Here we have the hydrodynamic radius estimate for the 3kDa dextran and 1.5 kDa dextran by the Zetasizer calculator, thanks to Alan.

Alan F Rawle, thank you so much for all your help