Sigma Notation Calculator

Use our free sigma notation calculator to evaluate Σ expressions: linear, quadratic, geometric, and power sums with custom bounds.

Math

Expression Type

Lower Bound (i = m)

Upper Bound (i = n)

Coefficient a

Coefficient b

Coefficient c

Ratio r

Exponent k

Formula

Sigma (Σ) notation represents the sum of a function evaluated at integer values between a lower and upper bound. Supports linear, quadratic, geometric (a·rⁱ), and power (iᵏ) expressions.

Σᵢ₌ₘⁿ f(i) evaluates the sum of f(i) from m to n

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Select the expression type.
2Set the lower bound m and upper bound n.
3Enter the coefficients for the expression.
4Click Calculate to evaluate the sum.

Examples

Σ₁¹⁰ i (linear, a=1, b=0)

1.1+2+...+10 = 55

Result: 55

Σ₁⁵ 2ⁱ (geometric)

1.2+4+8+16+32 = 62

Result: 62

Σ₁⁵ i² (power, k=2)

1.1²+2²+3²+4²+5² = 55

Result: 55

Frequently Asked Questions

Σ represents the sum of f(i) for i = m to n.

i (always used as the variable).

Yes, i iterates over all integers from m to n.

Up to 10,000 terms.

Built-in patterns: linear, quadratic, geometric, power.

Related Calculators

Arithmetic Series Calculator Geometric Series Calculator Harmonic Series Calculator Recursive Sequence Calculator Percentage Calculator Basic Calculator

CalculateMe Team

Last updated: 2026-07-14

Sigma Notation Calculator

Formula

How It Works

Examples

Σ₁¹⁰ i (linear, a=1, b=0)

Σ₁⁵ 2ⁱ (geometric)

Σ₁⁵ i² (power, k=2)

Frequently Asked Questions

What is sigma notation?

What is the index variable?

Can bounds be negative?

What is the max range?

What about custom expressions?

Related Calculators

Sigma Notation Calculator

Formula

How It Works

Examples

Σ₁¹⁰ i (linear, a=1, b=0)

Σ₁⁵ 2ⁱ (geometric)

Σ₁⁵ i² (power, k=2)

Frequently Asked Questions

What is sigma notation?

What is the index variable?

Can bounds be negative?

What is the max range?

What about custom expressions?

Related Calculators