Square Number Pyramid Pattern in PHP

Beginner

⏱️ 8 min read

📚 Updated: Aug 2026

🎯 3 Code Examples

🚀 Live Preview

Nested Loops + Formatting

Centered square number pyramid output in PHP (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, printf, a live preview, algorithm steps, worked PHP 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

printf("%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 PHP you use an outer loop with odd widths ($i = 1, 3, 5, …), a space loop for centering, and an inner loop that prints printf("%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 printf("%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.

PHP

// $rows = 3 (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	`(int) trim(fgets(STDIN));`	Flexible console programs
Cube variant	`printf("%4d", $m * $m * $m)`	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++) echo " ";`
Print squares	`printf("%4d", $m * $m); $m++;`
End the row	`echo PHP_EOL;`
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 PHP 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 fgets(STDIN) 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 PHP programs — fixed row count, fgets(STDIN) 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.

PHP

<?php
$rows = 5;
$maxOdd = 2 * $rows - 1;

$m = 1;
for ($i = 1; $i <= $maxOdd; $i += 2) {
    for ($j = $i; $j < $maxOdd; $j++) {
        echo "  ";
    }
    for ($k = 1; $k <= $i; $k++) {
        printf("%4d", $m * $m);
        $m++;
    }
    echo PHP_EOL;
}

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 trim(fgets(STDIN)) (check is_numeric() in real apps).

PHP

<?php
echo "Enter the number of rows: ";
$input = trim(fgets(STDIN));
if (!is_numeric($input)) {
    echo "Invalid input." . PHP_EOL;
    exit(1);
}
$rows = (int) $input;
$maxOdd = 2 * $rows - 1;

$m = 1;
for ($i = 1; $i <= $maxOdd; $i += 2) {
    for ($j = $i; $j < $maxOdd; $j++) {
        echo "  ";
    }
    for ($k = 1; $k <= $i; $k++) {
        printf("%4d", $m * $m);
        $m++;
    }
    echo PHP_EOL;
}

How It Works

Same nested-loop core as Example 1; only the source of $rows changes. Non-numeric input fails is_numeric() — validate before casting to int 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.

PHP

<?php
$rows = 3;
$maxOdd = 2 * $rows - 1;

$m = 1;
for ($i = 1; $i <= $maxOdd; $i += 2) {
    for ($j = $i; $j < $maxOdd; $j++) {
        echo "  ";
    }
    for ($k = 1; $k <= $i; $k++) {
        printf("%4d", $m * $m * $m);
        $m++;
    }
    echo PHP_EOL;
}

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

Set $rows = 5; and use fgets(STDIN) when reading input. Set $maxOdd, $m, and loop variables $i, $j, $k.

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)

printf("%4d", $m * $m) in a $k = 1..$i loop; increment $m, then echo PHP_EOL.

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 echo vs echo PHP_EOL without complex math.

Example: put echo PHP_EOL 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 fgets(STDIN) 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 PHP 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/$k for loops — or rename to $row/$col.
2. Prefer fgets(STDIN)
Avoid crashes when the user types letters instead of a number.
3. Keep echo PHP_EOL Outside
Only call echo PHP_EOL after the inner loop finishes the row.
4. Use Ternary for Compact Code
Store $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 echo PHP_EOL inside the inner loop.

Common Pitfalls

Mistakes that commonly break square number pyramids.

1. echo PHP_EOL Inside the Inner Loop
Each digit lands on its own line — you get a column, not a triangle.
→ Use printf("%4d", $m * $m) or echo for values; echo PHP_EOL 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 echo PHP_EOL glues every digit onto one endless line.
→ Always end the row after the inner loop.
4. Unchecked STDIN input
Letters or empty input leave $rows uninitialized.
→ Prefer fgets(STDIN) and re-prompt on failure.
5. Unformatted Numbers
Printing bare $m * $m without %4d breaks column alignment once values reach three digits.
→ Use printf("%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 STDIN input

Unchecked fgets(STDIN) leaves $rows unset — call is_numeric($input) 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 printf("%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 echo PHP_EOL 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 printf("%4d", $m * $m) and echo PHP_EOL after each row
Validate $rows ≥ 1 for interactive programs
Check fgets(STDIN) return value before using $rows
State O(n²) time when asked about complexity

❌ Don’t

Call echo PHP_EOL 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 printf("%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 trim(fgets(STDIN)) and check is_numeric($input) before casting to int.

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

Square Number Pyramid Pattern in PHP

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 fgets(STDIN)

3. Keep echo PHP_EOL Outside

4. Use Ternary for Compact Code

5. Dry-Run One Small n

Common Pitfalls

1. echo PHP_EOL Inside the Inner Loop

2. Wrong Space Loop

3. Forgetting the Row Break

4. Unchecked STDIN input

5. Unformatted Numbers

Edge Cases

Single digit

Empty pattern

$rows < 0

Many rows

Non-numeric STDIN 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 `fgets(STDIN)`

`$rows < 0`