Pell Number Calculator

Use our free Pell number calculator to generate the Pell sequence, test if a number belongs, or compute Pₙ for a given n.

Math

Mode

How Many

Number

Position (n)

Formula

Pell numbers follow the recurrence Pₙ = 2Pₙ₋₁ + Pₙ₋₂ with P₀ = 0 and P₁ = 1. The first few are 0, 1, 2, 5, 12, 29, 70, 169, ...

P₀ = 0, P₁ = 1, Pₙ = 2Pₙ₋₁ + Pₙ₋₂

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Select a mode: generate, check, or position.
2Click Calculate to see the result.

Examples

First 5 Pell

1.P₀=0, P₁=1, P₂=2, P₃=5, P₄=12

Result: 12

Check 29

1.29 = P₅, 29 is a Pell number

Result: Yes

P₇

1.P₇ = 169

Result: 169

Frequently Asked Questions

A sequence defined by Pₙ = 2Pₙ₋₁ + Pₙ₋₂, with P₀=0, P₁=1.

Pₙ/Pₙ₋₁ approaches 1+√2 ≈ 2.414 (the silver ratio).

Approximating √2, integer solutions to x²-2y²=±1.

P₀ = 0 by definition.

Pell numbers grow faster than Fibonacci, roughly doubling each step.

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CalculateMe Team

Last updated: 2026-07-14

Pell Number Calculator

Formula

How It Works

Examples

First 5 Pell

Check 29

P₇

Frequently Asked Questions

What are Pell numbers?

Relation to silver ratio?

Applications?

P₀?

Growth?

Related Calculators

Pell Number Calculator

Formula

How It Works

Examples

First 5 Pell

Check 29

P₇

Frequently Asked Questions

What are Pell numbers?

Relation to silver ratio?

Applications?

P₀?

Growth?

Related Calculators