Increase Precision of Numeric Calculations

By default, MATLAB® uses 16 digits of precision. For higher precision, use the vpa function in Symbolic Math Toolbox™. vpa provides variable precision which can be increased without limit.

When you choose variable-precision arithmetic, by default, vpa uses 32 significant decimal digits of precision. For details, see Choose Numeric or Symbolic Arithmetic. You can set a higher precision by using the digits function.

Approximate a sum using the default precision of 32 digits. If at least one input is wrapped with vpa, all other inputs are converted to variable precision automatically.

vpa(1/3) + 1/2
ans =
0.83333333333333333333333333333333

You must wrap all inner inputs with vpa, such as exp(vpa(200)). Otherwise, the inputs are automatically converted to double by MATLAB.

Increase the precision to 50 digits by using digits and save the old value of digits in digitsOld. Repeat the sum.

digitsOld = digits(50);
sum50 = vpa(1/3) + 1/2
sum50 =
0.83333333333333333333333333333333333333333333333333

Restore the old value of digits for further calculations.

digits(digitsOld)

Note

vpa output is symbolic. To use symbolic output with a MATLAB function that does not accept symbolic values, convert symbolic values to double precision by using double.

Check the current digits setting by calling digits.

digits
Digits = 32

Change the precision for a single vpa call by specifying the precision as the second input to vpa. This call does not affect digits. For example, approximate pi with 100 digits.

vpa(pi,100)
ans =
3.14159265358979323846264338327950288419716939937510582097494
4592307816406286208998628034825342117068
digits	% digits remains 32
Digits = 32

Variable precision can be increased arbitrarily. Find pi to 500 digits.

digitsOld = digits(500);
vpa(pi)
digits(digitsOld)
ans =
3.1415926535897932384626433832795028841971693993751058209749
445923078164062862089986280348253421170679821480865132823066
470938446095505822317253594081284811174502841027019385211055
596446229489549303819644288109756659334461284756482337867831
652712019091456485669234603486104543266482133936072602491412
737245870066063155881748815209209628292540917153643678925903
600113305305488204665213841469519415116094330572703657595919
530921861173819326117931051185480744623799627495673518857527
248912279381830119491

digits and vpa control the number of significant decimal digits. For example, approximating 1/111 with four-digit accuracy returns six digits after the decimal point because the first two digits are zeros.

vpa(1/111,4)
ans =
0.009009

Note

If you want to increase performance by decreasing precision, see Increase Speed by Reducing Precision.