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Sigma notation calculator (summation)

Evaluate a summation ∑ f(n) from a lower to an upper index. Type any expression in n — powers, fractions, factorials, trig, exponentials — set the bounds, and it computes the exact sum plus a term-by-term breakdown, live as you type.

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Sigma notation calculator (summation) is free to use as often as you like, directly from this page. Its place is under Numbers & arithmetic; Product notation calculator (pi notation) and Scientific notation converter answer the questions closest to this one.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Sigma notation calculator (summation) do?

Evaluate a summation ∑ f(n) from a lower to an upper index. Type any expression in n — powers, fractions, factorials, trig, exponentials — set the bounds, and it computes the exact sum plus a term-by-term breakdown, live as you type.

What does a concrete case look like?

Σ (k = 1 → 10) k = 55 — the tool shows every step in between, not just the final figure.

When would I actually use this?

Reading a number written another way: a Roman numeral on a monument, a hexadecimal colour, a binary byte, or a fraction that needs reducing.

What is the most common mistake?

Assuming a decimal fraction survives a change of base. A tenth is exact in decimal and infinitely repeating in binary, which is why 0.1 + 0.2 is not 0.3 in most programming languages.

How is Sigma notation calculator (summation) different from Product notation calculator (pi notation)?

They sit next to each other but answer different questions. Product notation calculator (pi notation): evaluate a product ∏ f(n) from a lower to an upper index — the multiplicative sibling of summation. Type any expression in n, set the bounds, and it computes the exact product with a term-by-term breakdown. Great for factorials, Wallis-type products and telescoping products. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Scientific notation converter is the closest one after this: Convert a number into scientific notation (mantissa × 10ⁿ).

Where do the figures come from?

Base conversion and number-theory results are exact. Roman numerals follow the standard subtractive form used since the Middle Ages, which is not the only one the Romans themselves used.

Further reading

All guides →
How-toScientific Notation ExplainedScientific notation writes huge and tiny numbers as a value times a power of ten. Here's how to write it, read the exponent, and convert back.ExplainerThe Pythagorean Theorem ExplainedIn a right triangle, a² + b² = c². Here's what the formula means, a worked example, how to find any side, and where it's used in real life.ExplainerRoman Numerals ExplainedSeven letters, added or subtracted. Here's what each stands for, how the subtractive pairs work, how to write any number, and where they still appear.ExplainerThe Advertised Rate Describes Almost None of What HappensWith a 0.6 % base rate, a soft pity at 74 and a hard pity at 90, the effective chance climbs from 0.6 % to 36.6 % by pull 80 and 90.6 % by pull 89. Without pity, ninety pulls would give 41.8 %.How-toHow to Round Numbers: Round Half Up, Round Half to Even, and MoreRound to any decimal place or number of significant figures, and learn when to use round half up versus round half to even to avoid bias.ExplainerSignificant Figures Explained: Counting, Rounding, and Why They MatterLearn what counts as a significant figure, the rules for leading, trailing, and captive zeros, and how sig figs keep your calculated answers honest.