# How to substitute a value for a symbolic variable

## Description

If we’ve defined a symbolic variable and used it in a formula, how can we substitute a value in for it, to evaluate the formula? This is often informally called “plugging in” a value.

Related tasks:

## Using SymPy, in Python

This answer assumes you have imported SymPy as follows.

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from sympy import * # load all math functions
init_printing( use_latex='mathjax' ) # use pretty math output

Let’s assume we’ve defined a variable and created a formula, as covered in how to create symbolic variables.

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var( 'x' )
formula = x**2 + x
formula

$\displaystyle x^{2} + x$

We can substitute a value for $x$ using the `subs`

function.
You provide the variable and the value to substitute.

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formula.subs( x, 8 ) # computes 8**2 + 8

$\displaystyle 72$

If you had to substitute values for multiple variables, you can use
multiple `subs`

calls or you can pass a dictionary to `subs`

.

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var( 'y' )
formula = x/2 + y/3
formula

$\displaystyle \frac{x}{2} + \frac{y}{3}$

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formula.subs( x, 10 ).subs( y, 6 )

$\displaystyle 7$

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formula.subs( { x: 10, y: 6 } )

$\displaystyle 7$

Content last modified on 24 July 2023.

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