PHP Math

PHP includes a set of built-in mathematical functions and constants for everyday calculations — absolute values, minimums and maximums, powers and roots, rounding, logarithms, trigonometry, and base conversion. They are part of the PHP core, so no extension needs to be installed.

This lesson explains the most useful functions, shows how they behave with different inputs, and applies them to real calculations: discounts, percentage changes, compound interest, loan EMIs, distances, and statistics.

Related lessons: Integer behavior (division, modulo, overflow) is covered in PHP Numbers; float precision and rounding modes in PHP Floats; secure random numbers in PHP Random Numbers.

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Overview of Common Math Functions

Function	Purpose	Example	Result
abs($n)	Absolute value (distance from zero)	abs(-7.5)	7.5
max(...) / min(...)	Largest / smallest value	max(3, 9, 2)	9
round($n, $p)	Round to precision	round(3.456, 2)	3.46
floor($n) / ceil($n)	Round down / up	ceil(4.1)	5
intdiv($a, $b)	Integer division	intdiv(17, 5)	3
fmod($a, $b)	Float remainder	fmod(7.5, 2)	1.5
sqrt($n)	Square root	sqrt(144)	12
pow($b, $e) / **	Power	2 ** 10	1024
exp($n)	e raised to a power	exp(1)	2.718281828459
log($n, $base)	Logarithm (natural by default)	log(8, 2)	3
log10($n)	Base-10 logarithm	log10(1000)	3
hypot($x, $y)	Length of the hypotenuse	hypot(3, 4)	5
pi() / M_PI	π	M_PI	3.1415926535898
deg2rad() / rad2deg()	Convert angles	deg2rad(180)	3.1415926535898
sin(), cos(), tan() …	Trigonometry (radians)	sin(deg2rad(30))	0.5
array_sum() / array_product()	Sum / product of an array	array_sum([1, 2, 3])	6
base_convert()	Convert between bases 2–36	base_convert("ff", 16, 2)	"11111111"

The "Result" column shows the values as echo prints them. Many of these functions return floats even when the result looks whole, as explained below.

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Absolute Value: abs()

abs() returns the distance of a number from zero — always non-negative.

<?php
echo abs(-15) . "\n";
echo abs(15) . "\n";
echo abs(-7.5) . "\n";

$budget = 5000;
$spent = 6250;
$difference = $budget - $spent;

echo "Over budget by ₹" . abs($difference) . "\n";

Output

15
15
7.5
Over budget by ₹1250

abs() keeps the type of its argument: an int stays an int, a float stays a float. It is typically used when the size of a difference matters but not its direction — temperature changes, distances between values, or tolerance checks such as abs($a - $b) < 0.001.

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Minimum and Maximum: min() and max()

Syntax

max(mixed $value, mixed ...$values): mixed
max(array $values): mixed

Both functions accept either several arguments or a single array.

Example

<?php
echo max(4, 12, 7) . "\n";
echo min(4, 12, 7) . "\n";

$prices = [1299, 499, 2499, 899];
echo "Highest: " . max($prices) . "\n";
echo "Lowest: " . min($prices) . "\n";

Output

12
4
Highest: 2499
Lowest: 499

Clamping a Value Into a Range

Combining min() and max() keeps a value within limits — one of the most common uses in real code:

<?php
function clamp(int|float $value, int|float $minimum, int|float $maximum): int|float
{
    return max($minimum, min($maximum, $value));
}

echo clamp(150, 1, 100) . "\n";
echo clamp(-5, 1, 100) . "\n";
echo clamp(42, 1, 100) . "\n";

Output

100
1
42

min($maximum, $value) caps the value at the maximum; max($minimum, ...) raises it to at least the minimum. Typical uses: page numbers, quantities, volume levels, percentages, and items-per-page settings from user input.

Things to Know

• Empty arrays throw an error. max([]) throws a ValueError in PHP 8 ("must contain at least one element"). Check $array !== [] first.
• Mixed types are compared with PHP's standard comparison rules, which can be surprising (for example, numeric strings compare as numbers, other strings alphabetically). Keep the values to a single type.

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Powers and Roots

Example

<?php
echo 2 ** 10 . "\n";
echo pow(5, 3) . "\n";
echo 9 ** 0.5 . "\n";
echo sqrt(144) . "\n";
echo 27 ** (1 / 3) . "\n";
var_dump(sqrt(144));
var_dump(2 ** 10);

Output

1024
125
3
12
3
float(12)
int(1024)

How It Works

• ** is the exponentiation operator; pow() is the equivalent function.
• An integer base with a non-negative integer exponent returns an int (unless it overflows). Fractional exponents produce floats.
• A fractional exponent calculates roots: ** 0.5 is the square root, ** (1/3) the cube root.
• sqrt() always returns a float, even for perfect squares — var_dump(sqrt(144)) shows float(12).
• sqrt() of a negative number returns NAN.

Note: ** is right-associative: 2 ** 3 ** 2 means 2 ** (3 ** 2) = 2 ** 9 = 512, not (2 ** 3) ** 2 = 64. Use parentheses to make the order clear.

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Logarithms and Exponentials

<?php
echo log(M_E) . "\n";        // natural logarithm (base e)
echo log10(1000) . "\n";     // base 10
echo log(8, 2) . "\n";       // base 2
echo exp(1) . "\n";          // e¹
echo log(1) . "\n";

Output

1
3
3
2.718281828459
0

• log($n) with one argument is the natural logarithm (base e). The second argument sets another base.
• exp($n) is e raised to the power $n; it is the inverse of log().
• log(0) returns -INF, and the logarithm of a negative number returns NAN.

Logarithms are used for growth calculations ("how many years until an investment doubles?"), scaling values for charts, and measuring orders of magnitude.

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Trigonometry and Angles

PHP's trigonometric functions use radians, not degrees. Convert with deg2rad() and rad2deg().

<?php
echo M_PI . "\n";
echo rad2deg(M_PI) . "\n";
echo sin(deg2rad(30)) . "\n";
echo cos(deg2rad(60)) . "\n";
var_dump(sin(deg2rad(30)));

Output

3.1415926535898
180
0.5
0.5
float(0.49999999999999994)

echo prints 0.5, but var_dump() reveals the actual stored value 0.49999999999999994. This is normal floating-point behavior: π cannot be stored exactly, so trigonometric results are approximations. Round results for display, and compare with a tolerance (see PHP Floats).

Available functions include sin(), cos(), tan(), asin(), acos(), atan(), atan2(), and hyperbolic versions such as sinh().

Useful Math Constants

Constant	Value	Meaning
M_PI	3.14159…	π
M_E	2.71828…	Euler's number e
M_SQRT2	1.41421…	√2
M_PI_2	1.57079…	π/2
M_LN2	0.69314…	Natural log of 2

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Remainders With Floats: fmod()

The % operator works with integers only. For decimal values, use fmod():

<?php
var_dump(fmod(7.5, 2));
var_dump(fmod(10, 3));
var_dump(fmod(-7.5, 2));

Output

float(1.5)
float(1)
float(-1.5)

Like %, the sign of the result follows the first argument. A common use is wrapping angles or time values, such as fmod($degrees, 360).

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Sums and Products of Arrays

<?php
$cart = [19.5, 250, 80.25];
$dimensions = [2, 3, 4];

echo array_sum($cart) . "\n";
echo array_product($dimensions) . "\n";
echo array_sum([]) . "\n";

Output

349.75
24
0

• array_sum() adds all values; an empty array returns 0.
• array_product() multiplies all values; an empty array returns 1.
• Both work on the array values. Non-numeric values are not silently ignored in recent PHP versions: since PHP 8.3, unsupported values (such as arrays or objects) produce a warning.

To sum one field from a list of records, combine with array_column():

<?php
$items = [
    ['name' => 'Pen', 'price' => 15, 'qty' => 10],
    ['name' => 'Notebook', 'price' => 60, 'qty' => 3],
];

echo array_sum(array_column($items, 'qty')) . " items\n";

Output

13 items

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Base Conversion

Function	Converts
decbin(), dechex(), decoct()	Decimal → binary / hexadecimal / octal string
bindec(), hexdec(), octdec()	Binary / hexadecimal / octal string → number
base_convert($str, $from, $to)	Any base 2–36 → any base 2–36

<?php
echo dechex(255) . "\n";
echo hexdec("ff") . "\n";
echo base_convert("ff", 16, 2) . "\n";
echo base_convert("255", 10, 36) . "\n";

Output

ff
255
11111111
73

Base 36 uses the digits 0–9 and letters a–z, which produces short identifiers: 255 is 7 × 36 + 3, written 73. URL shorteners use similar encodings to turn numeric IDs into compact codes.

Note: base_convert() works with floats internally and loses precision for very large numbers. Use GMP (gmp_strval(gmp_init($str, $from), $to)) for large values.

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Practical Calculations

Discounts and Percentages

<?php
$price = 999;
$discountPercent = 15;

$discount = $price * $discountPercent / 100;
$finalPrice = $price - $discount;

printf("Discount: ₹%.2f\n", $discount);
printf("Final price: ₹%.2f\n", $finalPrice);

$oldVisitors = 1200;
$newVisitors = 1500;
$change = ($newVisitors - $oldVisitors) / $oldVisitors * 100;

printf("Visitor change: %+.1f%%\n", $change);

Output

Discount: ₹149.85
Final price: ₹849.15
Visitor change: +25.0%

• Percentage of a value: value × percent / 100.
• Percentage change: (new − old) / old × 100. The %+ format shows the sign, so a decrease would display as -12.5%.
• Guard against division by zero when the old value can be 0.

Compound Interest

<?php
$principal = 100000;
$annualRate = 0.08;
$years = 5;

$amount = $principal * (1 + $annualRate) ** $years;

echo "Amount after $years years: ₹" . number_format($amount, 2) . "\n";
echo "Interest earned: ₹" . number_format($amount - $principal, 2) . "\n";

Output

Amount after 5 years: ₹146,932.81
Interest earned: ₹46,932.81

The formula is A = P × (1 + r)^n, where P is the principal, r the annual rate, and n the number of years. ** performs the power.

Loan EMI (Equated Monthly Installment)

<?php
function monthlyEmi(float $principal, float $annualRatePercent, int $months): float
{
    $r = $annualRatePercent / 12 / 100;

    if ($r == 0.0) {
        return $principal / $months;
    }

    $factor = (1 + $r) ** $months;

    return $principal * $r * $factor / ($factor - 1);
}

$loan = 500000;
$emi = monthlyEmi($loan, 9, 60);
$totalPaid = $emi * 60;

echo "EMI: ₹" . number_format($emi, 2) . "\n";
echo "Total paid: ₹" . number_format($totalPaid, 2) . "\n";
echo "Total interest: ₹" . number_format($totalPaid - $loan, 2) . "\n";

Output

EMI: ₹10,379.18
Total paid: ₹622,750.66
Total interest: ₹122,750.66

How It Works

1. The annual rate (9%) is converted to a monthly decimal rate: 9 / 12 / 100 = 0.0075.
2. The EMI formula is P × r × (1 + r)^n / ((1 + r)^n − 1).
3. (1 + r)^n is calculated once and stored in $factor, which avoids repeating the same calculation.
4. A zero-interest loan would cause division by zero in the formula, so it is handled separately.

These results are suitable for display and estimates. For actual financial records, banks apply specific rounding rules per installment; such systems use integer paise or BCMath (see PHP Floats).

Distance Between Two Coordinates (Haversine Formula)

<?php
function distanceKm(float $lat1, float $lon1, float $lat2, float $lon2): float
{
    $earthRadiusKm = 6371;

    $dLat = deg2rad($lat2 - $lat1);
    $dLon = deg2rad($lon2 - $lon1);

    $a = sin($dLat / 2) ** 2
        + cos(deg2rad($lat1)) * cos(deg2rad($lat2)) * sin($dLon / 2) ** 2;

    return 2 * $earthRadiusKm * asin(sqrt($a));
}

$chennai = [13.0827, 80.2707];
$bengaluru = [12.9716, 77.5946];

echo round(distanceKm(...$chennai, ...$bengaluru), 1) . " km\n";

Output

290.2 km

How It Works

• The haversine formula calculates the shortest distance over the Earth's surface (the "as the crow flies" distance) between two latitude/longitude points.
• Coordinates are in degrees, so differences are converted to radians with deg2rad() before using sin() and cos().
• ...$chennai unpacks the array into separate arguments (see Variadic Functions).
• The Earth's mean radius is about 6371 km. Road distance is longer; this formula gives straight-line distance, which is used for "stores near you" features and delivery radius checks.

Basic Statistics

<?php
function mean(array $values): float
{
    return array_sum($values) / count($values);
}

function median(array $values): float
{
    sort($values);
    $count = count($values);
    $middle = intdiv($count, 2);

    return $count % 2 === 0
        ? ($values[$middle - 1] + $values[$middle]) / 2
        : $values[$middle];
}

function standardDeviation(array $values): float
{
    $avg = mean($values);
    $squaredDiffs = array_map(fn($v) => ($v - $avg) ** 2, $values);

    return sqrt(array_sum($squaredDiffs) / count($values));
}

$deliveryDays = [12, 15, 11, 18, 14];

echo "Mean: " . mean($deliveryDays) . "\n";
echo "Median: " . median($deliveryDays) . "\n";
echo "Std deviation: " . round(standardDeviation($deliveryDays), 2) . "\n";

Output

Mean: 14
Median: 14
Std deviation: 2.45

How It Works

• Mean — the sum divided by the count (70 / 5 = 14).
• Median — the middle value after sorting (11, 12, 14, 15, 18 → 14). For an even count, it is the average of the two middle values. The median is less affected by extreme values than the mean.
• Standard deviation — how far values typically spread from the mean. Each difference from the mean is squared, the squares are averaged, and the square root of that average is taken. This is the population standard deviation.
• sort() inside median() works on a copy, because arrays are passed by value; the caller's array keeps its original order.
• These functions assume a non-empty array. In production code, check for empty input first to avoid DivisionByZeroError.

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Common Mistakes

Passing Degrees to Trigonometric Functions

Effect: sin(30) treats 30 as radians and returns about -0.988.

Fix: sin(deg2rad(30)).

Expecting Integer Results From sqrt(), round(), floor(), or ceil()

Effect: The result is a float, which can cause type errors or deprecation notices when used as an array index or an int argument.

Fix: Cast explicitly: (int) sqrt(144), (int) ceil($x).

Calling max() or min() on an Empty Array

Effect: ValueError in PHP 8.

Fix: Check that the array is not empty, or provide a default value.

Forgetting Division-by-Zero Cases

Effect: DivisionByZeroError in percentage changes, averages, and formulas with a rate of zero.

Fix: Handle zero denominators explicitly, as in monthlyEmi().

Using % With Decimals

Effect: 7.5 % 2 converts operands to integers (with a deprecation notice since PHP 8.1) and returns 1, not 1.5.

Fix: Use fmod().

Relying on Float Results for Money

Effect: Small rounding differences in totals and installments.

Fix: Format for display only; use integers in the smallest unit or BCMath for stored financial values.

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Best Practices

• Use max(min, min(max, value)) to clamp user input into valid ranges.
• Convert degrees to radians before using trigonometric functions.
• Round only when displaying results; keep full precision during calculations.
• Guard every division against a zero denominator.
• Use array_sum() with array_column() to total fields from records.
• Use BCMath or GMP when exact decimal results or very large numbers are required.

Official reference: https://www.php.net/manual/en/ref.math.php