Integral sign

An elongated S indicating integration in calculus.

Also known as: Integration symbol, Long S, Calculus S symbol

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Meanings

The integral sign denotes integration. Leibniz introduced it as an elongated S for the Latin 'summa', because an integral is the limit of a sum.

Common modern usageVerified fact
Denotes integration — the area under a curve, or more generally the accumulation of a quantity.
Contexts: Mathematics
Historically documentedDocumented interpretation
Was introduced by Leibniz as an elongated letter S standing for the Latin 'summa', reflecting that an integral is the limit of a sum.
Late 17th century onward · Contexts: Mathematics

A tall, narrow S-shaped curve stretched vertically, hooking outwards at the top and the bottom.

Used alongside: Summation sign
Continuous integration against discrete summation.

IdentityHigh confidence: High confidence because the identity is defined by a current official standard.
Historical originLow confidence: Low confidence because the historical origin is documented in encyclopedic references, but only a single source has been found so far, but the regional or cultural match to this specific claim is not precise.
Visual matchHigh confidence: High confidence because the visual match is defined by a current official standard.

Integral symbol
Wikipedia · retrieved 2026-07-30
Tertiary reference. Used for widely-agreed identity and origin summary, not for contested detail or exact dates.
Unicode Code Chart: Mathematical Operators (U+2200–U+22FF)
The Unicode Consortium · retrieved 2026-07-30
Authoritative for the character's code point, name and block only. Unicode assigns identity; it does not define what a symbol means in use.

Last reviewed 2026-07-30

Meanings

The integral sign denotes integration. Leibniz introduced it as an elongated S for the Latin 'summa', because an integral is the limit of a sum.

Common modern usageVerified fact

Denotes integration — the area under a curve, or more generally the accumulation of a quantity.

Historically documentedDocumented interpretation

Was introduced by Leibniz as an elongated letter S standing for the Latin 'summa', reflecting that an integral is the limit of a sum.

Late 17th century onward · Contexts: Mathematics

Confidence

IdentityHigh confidence: High confidence because the identity is defined by a current official standard.
Historical originLow confidence: Low confidence because the historical origin is documented in encyclopedic references, but only a single source has been found so far, but the regional or cultural match to this specific claim is not precise.
Visual matchHigh confidence: High confidence because the visual match is defined by a current official standard.

Sources

Integral symbol
Wikipedia · retrieved 2026-07-30
Tertiary reference. Used for widely-agreed identity and origin summary, not for contested detail or exact dates.
Unicode Code Chart: Mathematical Operators (U+2200–U+22FF)
The Unicode Consortium · retrieved 2026-07-30
Authoritative for the character's code point, name and block only. Unicode assigns identity; it does not define what a symbol means in use.

Last reviewed 2026-07-30