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GeezerVison is showing reference.wolfram.com — StandardForm—Wolfram Documentation

StandardForm[expr]

prints as the standard Wolfram Language two-dimensional representation of expr.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Basic Objects  
Special Input Forms  
Special Output Forms  
Properties & Relations  
Possible Issues  
Neat Examples  
See Also
Tech Notes
Related Guides
Related Links
History
Cite this Page

StandardForm

StandardForm[expr]

prints as the standard Wolfram Language two-dimensional representation of expr.

Details

  • StandardForm generates output that gives a unique and unambiguous representation of Wolfram Language expressions, suitable for use as input. »
  • StandardForm incorporates many aspects of traditional mathematical notation.
  • StandardForm is the standard format type used for both input and output of Wolfram Language expressions in notebooks.
  • Graphics and Graphics3D are displayed graphically in StandardForm.
  • StandardForm can be edited in the notebook front end.
  • StandardForm uses special characters as well as ordinary keyboard characters.
  • StandardForm is based on boxes.
  • The notebook front end contains menu items for conversion to and from StandardForm.
  • When an input evaluates to StandardForm[expr], StandardForm does not appear in the output. »

Examples

open all close all

Basic Examples  (2)

StandardForm is used by default for output:

Wolfram Language code: x ^ 2 + x ^ (-1) + Pi
Wolfram Language code: x ^ 2 + x ^ (-1) + Pi//StandardForm

StandardForm for graphics:

Wolfram Language code: Graphics[{Red, Disk[]}]
Wolfram Language code: Graphics3D[Sphere[]]

Scope  (7)

Basic Objects  (2)

Integer, Rational, Real, and Complex numbers:

Wolfram Language code: Map[StandardForm, {123, 1 / 23, 1.23, 1 + 23I}]

Arbitrary-precision Real and Complex numbers:

Wolfram Language code: StandardForm /@ N[{10 / 3, 10 / 3I}, 20]

Special constants:

Wolfram Language code: StandardForm /@ {I, Pi, E}

Characters and strings of characters:

Wolfram Language code: StandardForm /@ {"a", "α", "⊕"}

Control characters for strings:

Wolfram Language code: StandardForm["A first line A second line"]

Special Input Forms  (3)

Different Power expressions:

Wolfram Language code: StandardForm /@ {a ^ x, a^(1/(3)), Exp[x], x^-1}

Special typeset expressions:

Wolfram Language code: StandardForm /@ {Subscript[∂, x]y[x], Integrate[y[x], x], Sum[y[k], {k, 1, n}], Element[x, Reals], (x∧y)∨z}

Different list structures:

Wolfram Language code: StandardForm /@ {(| | | | | - | - | - | | a | b | c | | d | e | f |), (| | | | ------------------------------------------------------- | -------------------------------------------------------- | | (⁠\| \| \| \| - \| - \| \| a \| b \| \| c \| d \|⁠) | (⁠\| \| \| \| - \| - \| \| a \| b \| \| c \| d \|⁠)⁠ | | (⁠\| \| \| \| - \| - \| \| a \| b \| \| c \| d \|⁠) | (⁠\| \| \| \| - \| - \| \| a \| b \| \| c \| d \|⁠) |)}

Special Output Forms  (2)

Some objects use a special output representation:

Wolfram Language code: StandardForm[ser = Series[Sin[x], {x, 0, 3}]]

Compare with the underlying FullForm of the expression:

Wolfram Language code: FullForm[ser]

Some objects use an elided output representation:

Wolfram Language code: StandardForm[i = Interpolation[{1, 2, 3, 1}]]
Wolfram Language code: StandardForm[s = SparseArray[{{1, 2} -> 1}, {5, 5}]]

The elided parts are visible using InputForm:

Wolfram Language code: InputForm[i]
Wolfram Language code: InputForm[s]

Properties & Relations  (5)

When an input evaluates to StandardForm[expr], StandardForm does not appear in the output:

Wolfram Language code: StandardForm[x ^ 2]

Out is assigned the value x2, not StandardForm[x^2]:

Wolfram Language code: %//FullForm

StandardForm is two-dimensional unambiguous formatting:

Wolfram Language code: StandardForm[Exp[I x / n]]

OutputForm approximates StandardForm using keyboard characters:

Wolfram Language code: OutputForm[Exp[I x / n]]

TraditionalForm is two-dimensional, but ambiguous formatting:

Wolfram Language code: TraditionalForm[Exp[I x / n]]

InputForm and FullForm provide one-dimensional formatting:

Wolfram Language code: InputForm[Exp[I x / n]]
Wolfram Language code: FullForm[Exp[I x / n]]

Use ToString to generate a string in StandardForm:

Wolfram Language code: ToString[a ^ b, StandardForm]

The string includes two-dimensional markup:

Wolfram Language code: FullForm[%]

Use ToExpression to convert back:

Wolfram Language code: ToExpression[%]
Wolfram Language code: FullForm[%]

Use ToBoxes to get the box representation of an expression in StandardForm:

Wolfram Language code: ToBoxes[x ^ 2 + y ^ 3, StandardForm]

Use ToExpression to convert back:

Wolfram Language code: ToExpression[%]

Add formatting via Format:

Wolfram Language code: bin[x, y]//StandardForm
Wolfram Language code: Format[bin[x_, y_], StandardForm] := MatrixForm[{{x}, {y}}]
Wolfram Language code: bin[x, y]//StandardForm

Possible Issues  (1)

Even when an output omits StandardForm from the top level, it is not stripped from subexpressions:

Wolfram Language code: e = StandardForm[x ^ 2]

The output does not have StandardForm in it:

Wolfram Language code: %

However, the variable e does have StandardForm in it, which may affect subsequent evaluations:

Wolfram Language code: FullForm[e]

The product is not evaluated due to the intervening StandardForm:

Wolfram Language code: x * e

Assign variables first and then apply StandardForm to the result to maintain computability:

Wolfram Language code: (f = x ^ 2)//StandardForm
Wolfram Language code: x * f

Neat Examples  (1)

Nested roots:

Wolfram Language code: Nest[Sqrt[1 + 1 / #]&, x, 10]

Nested powers:

Wolfram Language code: Nest[x ^ -#&, x, 10]

See Also

TraditionalForm  OutputForm  InputForm  Style  MakeExpression  ToBoxes

Tech Notes

    ▪
  • Forms of Input and Output
    • ▪
  • Reducing Expressions to Their Standard Form
    • ▪
  • The Interpretation of Textual Forms
    • ▪
  • The Representation of Textual Forms

Related Guides

    ▪
  • Mathematical Typesetting
    • ▪
  • Cell Menu
    • ▪
  • Converting between Expressions & Strings
    • ▪
  • Graphics Directives

Related Links

  • NKS|Online  (A New Kind of Science)

History

Introduced in 1996 (3.0) | Updated in 2007 (6.0)

Wolfram Research (1996), StandardForm, Wolfram Language function, https://reference.wolfram.com/language/ref/StandardForm.html (updated 2007).

Text

Wolfram Research (1996), StandardForm, Wolfram Language function, https://reference.wolfram.com/language/ref/StandardForm.html (updated 2007).

CMS

Wolfram Language. 1996. "StandardForm." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2007. https://reference.wolfram.com/language/ref/StandardForm.html.

APA

Wolfram Language. (1996). StandardForm. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/StandardForm.html

BibTeX

@misc{reference.wolfram_2026_standardform, author="Wolfram Research", title="{StandardForm}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/StandardForm.html}", note=[Accessed: 12-November-2026]}

BibLaTeX

@online{reference.wolfram_2026_standardform, organization={Wolfram Research}, title={StandardForm}, year={2007}, url={https://reference.wolfram.com/language/ref/StandardForm.html}, note=[Accessed: 12-November-2026]}
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