🔢Basic Maths Notation

3 Jun 2026

A reference for reading the symbols in formulas, written for people (me) who aren’t confident with maths. Most “scary” equations are just a recipe: do these operations, in this order, with these named ingredients.

The symbols you’ll meet most

Symbol	Name	Means	Example
`+ − × ÷`	plus, minus, times, divide	basic arithmetic	`3 × 4 = 12`
`=`	equals	left side has the same value as right	`Q = U × A`
`Σ`	sigma (capital)	sum: add up a series of things	see below
`Δ`	delta (capital)	change/difference between two values	`ΔT = 21 − (−3)`
`·`	dot	multiply (same as `×`)	`W/m²·K`
`²` `³`	superscript	a power: how many times to multiply by itself	`m² = m × m`
`√`	root	the opposite of a power	`√9 = 3`
`ⁿ` `ₓ`	super/subscript	a label or a power, depending on context	`x₁`, `2ⁿ`
`≈`	approximately equal	”about”, not exact	`π ≈ 3.14`
`∝`	proportional to	grows in step with	`cost ∝ size`

Σ — “sum of”

The capital Greek letter sigma means add all of these up. It looks intimidating but it’s just a loop.

Σ (U × A × ΔT)

reads as: for each item, work out U × A × ΔT, then add all those results together.

In code it’s a for loop with a running total:

// Σ (U × A × ΔT) for every wall/window/etc in a room
const total = surfaces.reduce(
  (sum, s) => sum + s.U * s.A * deltaT,
  0,
);

So a single Σ replaces “do this for the wall, the window, the roof, the floor… then add it all up”.

Δ — “the change in”

Capital delta means difference: end value minus start value.

ΔT = inside − outside = 21 − (−3) = 24

The two minus signs trip people up. Subtracting a negative is the same as adding:

21 − (−3)  =  21 + 3  =  24

ΔT is read “delta T” and almost always means a temperature difference.

Powers and roots

A small raised number is a power — how many times to multiply a number by itself:

m²  = m × m          (square — think area)
m³  = m × m × m      (cube — think volume)
2⁵  = 2 × 2 × 2 × 2 × 2 = 32

A root is the reverse. √9 = 3 because 3 × 3 = 9.

You’ll see powers most often in units (m² for area, m³ for volume), not just in equations.

Reading units: the `/` and `·`

Units carry meaning. Learn to read them aloud:

/ = “per”. m/s = metres per second.
· = multiply. W/m²·K = watts per (square-metre times kelvin).
K = kelvin. For a difference in temperature, 1 K = 1 °C, so ΔT in K and in °C are the same number.

When a unit looks busy, it’s usually telling you exactly what to multiply and divide:

U has units W/m²·K. Multiply it by an area (m²) and a temperature difference (K) and the m² and K cancel out, leaving W — watts, a rate of heat loss. The units are a built-in sanity check.

Worked example — heat loss from a room

Two formulas, both just “multiply the named things together”. Numbers from a real heat-loss calc.

1. Fabric loss — heat through walls/windows/roof/floor

Q_fabric = Σ (U × A × ΔT)

U = U-value (W/m²·K) — how leaky the material is. Triple glazing ≈ 0.8, solid brick ≈ 2.1. Higher = leakier.
A = area (m²)
ΔT = inside target − outside design temp, e.g. 21 − (−3) = 24 K
Q_fabric = the answer, in watts. (Q is the standard letter for “quantity of heat”; the small fabric is just a label, not maths.)

The Σ says: do U × A × ΔT for each surface, then add them.

const surfaces = [
  { name: 'wall',   U: 2.1, A: 12 },
  { name: 'window', U: 0.8, A: 3  },
];
const deltaT = 21 - -3; // 24

const qFabric = surfaces.reduce(
  (sum, s) => sum + s.U * s.A * deltaT,
  0,
);
// wall:   2.1 × 12 × 24 = 604.8 W
// window: 0.8 × 3  × 24 =  57.6 W
// total = 662.4 W

2. Ventilation loss — heat carried out by air leaving the room

Q_vent = 0.33 × ACH × V × ΔT

0.33 = volumetric heat capacity of air (Wh/m³·K) — a fixed constant.
ACH = air changes per hour (a lookup based on room type).
V = room volume (m³)
ΔT = same temperature difference as above.

No Σ here — it’s a single multiplication, left to right:

const qVent = 0.33 * ach * volume * deltaT;
// e.g. 0.33 × 1.5 × 30 × 24 = 356.4 W

Total heat the room loses = Q_fabric + Q_vent. That’s the size of radiator you need.

The trick for any formula

Name every symbol. A formula is a sentence — Q, U, A are just nouns with values.
Subscripts are labels, not maths. Q_fabric and Q_vent are two different Qs.
Σ means loop-and-add. Everything inside it happens once per item.
Units tell you the operations. If the answer should be watts and you’ve got watts, you did it right.
Work left to right, doing brackets ( ) first.

Once you can read it aloud in plain English, the maths is usually just multiplication.