Square Number Pyramid Pattern in Java

Beginner

⏱️ 8 min read

📚 Updated: Aug 2026

🎯 3 Code Examples

🚀 Live Preview

Nested Loops + Formatting

Centered square number pyramid output in Java (1, 4 9 16, 25 36 49 64 81, ...)

Overview

What You’ll Learn

The square number pyramid prints consecutive squares in a centered triangle with odd-width rows. This tutorial covers the three-loop row structure, System.out.format, a live preview, algorithm steps, worked Java examples, edge cases, and complexity.

Shape Rule

Odd widths, centered

Row widths are 1, 3, 5, … up to 2*rows-1; each value is m*m.

Space Loop

Center rows

for (j = i; j < maxOdd; j++) prints leading space pairs before each row.

Number Loop

m*m squares

System.out.format("%4d", m*m) prints i squares per row; m increments each time.

Outer Loop

i += 2

for (i = 1; i <= maxOdd; i += 2) walks odd row widths only.

Live Preview

1–20 rows

Pick a row count and draw the square number pyramid instantly in the browser.

O(n²)

Complexity

Total numbers = n²; extra memory stays O(1).

Introduction

A square number pyramid prints consecutive squares in a centered triangle. With rows = 5, the output starts with 1, then 4 9 16, building to a widest row of nine squared values.

In Java you use an outer loop with odd widths (i = 1, 3, 5, …), a space loop for centering, and an inner loop that prints System.out.format("%4d", m*m) while incrementing m.

Why it matters?

It teaches three nested loops on one row plus formatted output — a key step before hollow pyramids and diamonds.

Key Highlights

Odd Row Widths

Outer loop uses i = 1, 3, 5, … up to 2*rows-1.

Centered Rows

Leading space pairs shift smaller rows to the right.

Squared Values

Counter m prints m*m with %4d formatting.

Series Foundation

Follow Program 40 alternating 1/0; continue to Program 42 hollow square.

In short: for each odd width i up to 2*rows-1, print leading spaces, then print i squared values with System.out.format("%4d", m*m), incrementing m each time.

Foundation

📝 Problem & Approach

Given a positive integer rows (e.g. 5), print a centered pyramid of consecutive squares. Row widths are odd: 1, 3, 5, … up to 2*rows-1.

Java

// rows = 3 (conceptual shape — columns aligned with %4d)
//         1
//     4   9  16
// 25  36  49  64  81

Inputs & Outputs

Item	Type	Description
`rows`	int	Number of triangle lines to print (typically ≥ 1).
Printed output	text	Centered rows of squared integers; row width `i` prints `i` values.

Minimal workflow

Pseudocode

for i from 1 to 2*rows-1 step 2:
    print leading spaces (i .. maxOdd-1)
    repeat i times:
        print m*m with fixed width; m++
    print newline

Approach comparison

Approach	Idea	Best for
Three nested loops	`1`, then `4 9 16`, …	Learning and interviews
User-input rows	`sc.nextInt();`	Flexible console programs
Cube variant	`System.out.format("%4d", mmm)`	Extending the same structure

Cheat Sheet

⚡ Quick Reference

Goal	Pattern
Odd-width rows	`for (i = 1; i <= maxOdd; i += 2)`
Center with spaces	`for (j = i; j < maxOdd; j++) System.out.print(" ");`
Print squares	`System.out.format("%4d", m*m); m++;`
End the row	`System.out.println();`
Program 40 contrast	Alternating 1/0 uses parity; this pyramid uses odd widths + formatting

Compare

📋 Spaces vs Squares vs Combined

Same pyramid row — how the space loop and number loop work together.

Space loop

j = i..maxOdd-1

Leading pairs of spaces center each row

Number loop

k = 1..i

Prints m*m with %4d; increments m

Row width

odd i

Widths 1, 3, 5, … keep the pyramid symmetric

Learning tip

trace i=3

Dry-run row 3: spaces then three squares 4, 9, 16

Context

When This Pattern Shows Up

Reach for this pattern when teaching space alignment and one inner loop on the same row.

First lab exercise
Most Java pattern series start here before pyramids and diamonds.
Nested-loop warm-up
Outer/inner bound practice with an immediate visual check.
Console I/O practice
Combine loops with Scanner for a flexible row count.
Gateway to variants
Compare with Program 40 (alternating 1/0), then continue to Program 42 (hollow square).
Not a UI layout tool
This is a console teaching pattern — not how you build modern app screens.

Key benefit: one small program that locks in nested loops, output sequencing, and O(n²) thinking.

Interactive

🔮 Live Preview

Choose a row count between 1 and 20 and draw the square number pyramid in the browser.

Hands-On

Examples Gallery

Three complete Java programs — fixed row count, Scanner input, and a spaced-output variant. Click View Output to reveal sample console results.

📚 Getting Started

Print five rows with three nested loops per line.

Example 1 — Fixed `rows = 5`

Hard-coded size — three nested loops build each centered row of squares.

Java

public class SquareNumberPyramid {
    public static void main(String[] args) {
        int rows = 5;
        int maxOdd = 2 * rows - 1;

        int m = 1;
        for (int i = 1; i <= maxOdd; i += 2) {
            for (int j = i; j < maxOdd; j++) {
                System.out.print("  ");
            }
            for (int k = 1; k <= i; k++) {
                System.out.format("%4d", m * m);
                m++;
            }
            System.out.println();
        }
    }
}

How It Works

When i = 1, the space loop indents the row and one square 1 prints. When i = 3, three values appear: 4, 9, 16 — with m at 2, 3, 4.

📈 Practical Variant

Let the user choose the height at runtime.

Example 2 — User Input Version

Read the row count with Scanner.nextInt() (check hasNextInt() in real apps).

Java

import java.util.Scanner;

public class SquareNumberPyramidInput {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        System.out.print("Enter the number of rows: ");
        int rows = sc.nextInt();
        int maxOdd = 2 * rows - 1;

        int m = 1;
        for (int i = 1; i <= maxOdd; i += 2) {
            for (int j = i; j < maxOdd; j++) {
                System.out.print("  ");
            }
            for (int k = 1; k <= i; k++) {
                System.out.format("%4d", m * m);
                m++;
            }
            System.out.println();
        }

        sc.close();
    }
}

How It Works

Same nested-loop core as Example 1; only the source of rows changes. Non-numeric input throws InputMismatchException with nextInt() — check hasNextInt() for safer labs.

⚡ Readability Variant

Same pyramid structure printing cubes instead of squares.

Example 3 — Cube Pyramid

Replace m*m with m*m*m to print consecutive cubes in the same centered shape.

Java

public class SquareNumberPyramidCubes {
    public static void main(String[] args) {
        int rows = 3;
        int maxOdd = 2 * rows - 1;

        int m = 1;
        for (int i = 1; i <= maxOdd; i += 2) {
            for (int j = i; j < maxOdd; j++) {
                System.out.print("  ");
            }
            for (int k = 1; k <= i; k++) {
                System.out.format("%4d", m * m * m);
                m++;
            }
            System.out.println();
        }
    }
}

How It Works

Same loop structure; only the print expression changes to m*m*m for consecutive cubes.

🧠 How the Algorithm Prints Rows

Set up

System.out is built in; use Scanner when reading input. Set rows (fixed or from input).

Setup

Outer loop (odd widths)

for (i = 1; i <= maxOdd; i += 2) — row widths 1, 3, 5, … up to 2*rows-1.

Row

Space loop (center)

for (j = i; j < maxOdd; j++) prints leading space pairs before the numbers.

Width

Number loop (squares)

System.out.format("%4d", m*m) in a k = 1..i loop; increment m, then println().

Squares

Square number pyramid complete

Total number prints: n² — O(n²) time, O(1) extra memory.

Trace

🔎 Worked Walkthrough — `rows = 3`

Trace each odd width: leading spaces, values printed, and running counter m.

`i` (width)	Spaces (`j`)	`m` range	Squares printed
`1`	4 pairs	1	`1`
`3`	2 pairs	2–4	`4 9 16`
`5`	0 pairs	5–9	`25 36 49 64 81`

Total number prints: 1+3+5 = 9 = 3² = n².

Use Cases

Where this tiny pattern (and its loop structure) shows up beyond the homework prompt.

1. Teaching Nested Loops

Clearest visual proof that outer and inner bounds interact.

Example: change j <= i and watch the shape change.

2. Pattern Series Base

Foundation for inverted, pyramid, diamond, and hollow variants.

Example: change k start to 100 for a shifted sequence.

3. Console Formatting Drills

Practice System.out.print vs row newline without complex math.

Example: put System.out.println() inside the inner loop by mistake.

4. Character Substitution

Swap digits for letters, stars, or spaced output once the loop works.

Example: use %4d when values exceed two digits.

5. Complexity Intuition

Triangular totals make O(n²) concrete for beginners.

Example: count printed digits for n = 10 still → 55.

6. Input Validation Labs

Pair the pattern with Scanner and positive-row checks.

Example: reject rows <= 0 and re-prompt.

Pro Tip: when an interviewer asks for patterns, explain the outer/inner roles first — then write the loops. The story matters as much as the code.

Advantages

Why this pattern earns a permanent spot in beginner Java courses.

1. Instant Visual Feedback
Wrong bounds show up immediately as a broken staircase.
2. Minimal Concepts
Only loops and console output — no arrays or math libraries.
3. Easy to Extend
Invert, center, hollow, or change the fill character with small edits.
4. O(1) Extra Memory
Streaming output needs no storage beyond loop counters.

Pro Tip: learn the three-loop row version first; then try the cube variant in Example 3.

Usage Tips

Small habits that keep number-pattern code clean.

1. Name Bounds Clearly
Use rows (or n) and keep i/j for row/column — or rename to row/col.
2. Prefer Scanner
Avoid crashes when the user types letters instead of a number.
3. Keep System.out.println() Outside
Only call System.out.println() after the inner loop finishes the row.
4. Use Ternary for Compact Code
Store int sq = m * m; once per inner iteration when debugging row traces.
5. Dry-Run One Small n
Trace rows = 3 on paper before coding larger demos.

Pro Tip: if the output is a vertical list of single digits per line, you almost certainly put System.out.println() inside the inner loop.

Common Pitfalls

Mistakes that commonly break square number pyramids.

1. System.out.println() Inside the Inner Loop
Each digit lands on its own line — you get a column, not a triangle.
→ Use System.out.print for the digit; System.out.println() only after the inner loop.
2. Wrong Space Loop
Using j = 1..i for spaces pushes rows left instead of centering them.
→ Keep for (j = i; j < maxOdd; j++) to print the correct leading indent.
3. Forgetting the Row Break
Omitting System.out.println() glues every digit onto one endless line.
→ Always end the row after the inner loop.
4. Unchecked Scanner input
Letters or empty input throw undefined rows.
→ Prefer Scanner and re-prompt on failure.
5. Unformatted Numbers
Printing bare m*m without %4d breaks column alignment once values reach three digits.
→ Use System.out.format("%4d", m*m) or widen the field for larger pyramids.

Edge Cases

Check these inputs before calling the solution done.

rows = 1

Single digit

Output is just 1 on one line.

rows = 0

Empty pattern

Outer loop never runs — print nothing or show a message.

Negative

`rows < 0`

Treat as invalid; re-prompt instead of silent empty output.

Large n

Many rows

Output grows as n²/2 characters — fine for labs, noisy for huge n.

Bad input

Non-numeric Scanner input

Unchecked Scanner leaves rows unset — call sc.hasNextInt() first.

Fill char

Cube variant

Swap m*m for m*m*m — see Example 3.

Drill

🎯 Practice Problems

Try these variations to lock in the pattern.

1. Alternating 1/0 pattern

Parity check with shrinking width
Review Program 40

2. Hollow square of 1s

Border-only square with nested loops
Continue with Program 42

3. Cube pyramid

Replace m*m with m*m*m
Same three-loop structure

4. Wider formatting

Use %5d when squares exceed 999
Keep columns aligned for large rows

Important

Notes

Square count. Total prints for n rows is n² — odd widths sum to a perfect square.
print stays on the line; println advances — mix them carefully.
Validate rows > 0 for interactive programs; rows = 1 should print a single 1.
Use System.out.format("%4d", m*m) so columns stay aligned as values grow.

Quick Takeaway: odd-width outer loop, space loop for centering, number loop for m*m, then break the line.

Analysis

⏱️ Time and Space Complexity

Program	Time	Extra space
Nested loops (Examples 1–2)	`O(rows²)`	`O(1)`
Cube variant (Example 3)	`O(rows²)`	`O(1)`

Wrap Up

🎉 Conclusion

The square number pyramid combines an odd-width outer loop with a space loop and a number loop — a natural step after alternating 1/0 patterns. Master the fixed-rows version first, then try user input and the cube variant.

Practice the three examples above, then continue to Program 42 for the hollow square of 1s.

Row width i prints i squares — keep println() only after both inner loops finish.

View Examples Gallery Continue to Program 42

Pro Tips

💡 Best Practices

✅ Do

Explain odd widths, space loop, and m*m counter before coding
Use System.out.format("%4d", m*m) and println() after each row
Validate rows ≥ 1 for interactive programs
Check Scanner return value before using rows
State O(n²) time when asked about complexity

❌ Don’t

Call System.out.println() inside the inner digit loop
Skip the space loop (pyramid aligns left)
Print unformatted squares when alignment matters
Ignore bad console input in user-facing demos
Skip the rows = 1 edge case

Summary

Key Takeaways

Knowledge Unlocked

Five things to remember about this square number pyramid

Print the pattern the beginner-friendly way.

Core concepts

△ 01

Rule

Odd widths: 1, 3, 5…

Definition

↻ 02

Space loop

Centers each row

Code

↓ 03

Number loop

Prints m*m with %4d

Logic

n 04

Total prints

n² numbers

I/O

O 05

Complexity

O(n²) time

Analysis

❓ Frequently Asked Questions

Why does each row have an odd number of values?

Odd widths (1, 3, 5, …) keep the pyramid symmetric. The last row has 2*rows-1 numbers.

How are squared values generated?

A counter m starts at 1 and increments after every print. The program outputs m*m, producing 1, 4, 9, 16, 25, and so on.

How does the program center-align the pyramid?

Before printing numbers, a space loop runs from j=i to maxOdd-1, printing leading pairs of spaces so smaller rows shift right.

Why use System.out.format("%4d", m*m)?

Fixed-width columns keep alignment when values grow to three digits (121) or more.

Can I print cubes instead of squares?

Yes. Replace m*m with m*m*m — see Example 3.

What is the time complexity?

O(n²) for n rows because total printed numbers are 1+3+5+…+(2n-1) = n².

How should I read the row count safely?

Use sc.hasNextInt() before sc.nextInt() so bad input does not throw InputMismatchException.

What happens if rows is 0 or negative?

maxOdd becomes negative or zero and the outer loop never runs. Validate and prompt again for interactive programs.

Did you Know? 🔊

Each row prints an odd count of squared values (1, 3, 5, …). A counter m increments after every print and the program outputs m*m with fixed-width formatting — total numbers equal n² for n rows.

Continue to Program 42

Move on to the hollow square of 1s in the Java number-pattern series.

Program 42 tutorial →

About the author

Mari Selvan M P 🔗

Developer, cloud engineer, and technical writer

Experience 12 years building web and cloud systems
Focus Full Stack Development, AWS, and Developer Education

I write practical tutorials so students and working developers can learn by doing—from databases and APIs to deployment on AWS.

AWS Certified Developer – Associate (Credly)

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Java Number Pattern 40 — Alternating 1/0 Pattern Java Number Pattern 42 — Hollow Square of 1s

Square Number Pyramid Pattern in Java

What You’ll Learn

Shape Rule

Space Loop

Number Loop

Outer Loop

Live Preview

O(n²)

Introduction

Why it matters?

Odd Row Widths

Centered Rows

Squared Values

Series Foundation

📝 Problem & Approach

Inputs & Outputs

Minimal workflow

Approach comparison

⚡ Quick Reference

📋 Spaces vs Squares vs Combined

When This Pattern Shows Up

First lab exercise

Nested-loop warm-up

Console I/O practice

Gateway to variants

Not a UI layout tool

🔮 Live Preview

Examples Gallery

📚 Getting Started

Example 1 — Fixed rows = 5

How It Works

📈 Practical Variant

Example 2 — User Input Version

How It Works

⚡ Readability Variant

Example 3 — Cube Pyramid

How It Works

🧠 How the Algorithm Prints Rows

Set up

Outer loop (odd widths)

Space loop (center)

Number loop (squares)

Square number pyramid complete

🔎 Worked Walkthrough — rows = 3

Use Cases

1. Teaching Nested Loops

2. Pattern Series Base

3. Console Formatting Drills

4. Character Substitution

5. Complexity Intuition

6. Input Validation Labs

Advantages

1. Instant Visual Feedback

2. Minimal Concepts

3. Easy to Extend

4. O(1) Extra Memory

Usage Tips

1. Name Bounds Clearly

2. Prefer Scanner

3. Keep System.out.println() Outside

4. Use Ternary for Compact Code

5. Dry-Run One Small n

Common Pitfalls

1. System.out.println() Inside the Inner Loop

2. Wrong Space Loop

3. Forgetting the Row Break

4. Unchecked Scanner input

5. Unformatted Numbers

Edge Cases

Single digit

Empty pattern

rows < 0

Many rows

Non-numeric Scanner input

Cube variant

🎯 Practice Problems

1. Alternating 1/0 pattern

2. Hollow square of 1s

3. Cube pyramid

4. Wider formatting

Example 1 — Fixed `rows = 5`

🔎 Worked Walkthrough — `rows = 3`

2. Prefer `Scanner`

`rows < 0`