To explain an equation in a video, never put the whole thing on screen at once. Start with the question it answers, in words. Then build it one symbol at a time, saying what each symbol means and its unit as it appears. Once it is complete, say what the equation claims in one plain sentence ("pressure and volume trade off against each other"), check that the units on both sides match, and finish with one worked example using real numbers, every line shown. Close with a sanity check and the most common mistake. A finished equation shown all at once is read silently by the viewer, who then stops listening while you catch up.

What an equation is, on screen

An equation is a sentence written in symbols. PV = nRT says something you could write out in English: the pressure of a gas times its volume equals the amount of gas times a constant times the temperature.

That is why a video has an advantage over a textbook here. A textbook shows the compressed version and expects you to decompress it alone. A video can do the decompression in front of the viewer, in order, with a voice saying each part as it arrives. The skill is in the order.

It is the same idea as building a graph axis by axis before any data goes on it, which is covered in how to explain a graph in a video. An equation is built symbol by symbol before any number goes in.

The six beats of an equation explanation

Beats 1 and 3 are what most student videos skip. Beat 1 gives the symbols somewhere to land. Beat 3 is the proof that you understand the equation rather than recognise it.

Worked example: the ideal gas law, PV = nRT

The ideal gas law links four properties of a gas. It appears in GCSE and A level physics and chemistry, in first-year university courses, and in plenty of exam questions where students lose marks on units. Here is a scene list for a three minute video, about 450 words of narration.

Scene 1, the question. "If you know how much gas you have and how hot it is, how much space does it need? There is one equation that answers that for most gases in ordinary conditions." On screen: a sealed syringe of air, no symbols.

Scene 2, P. "P is pressure: how hard the gas pushes on its container. We measure it in pascals." On screen: P drawn, with arrows pushing outward on the syringe walls, and the label Pa.

Scene 3, V. "V is volume: the space the gas takes up, in cubic metres." On screen: P V, with the inside of the syringe shaded and labelled m³.

Scene 4, n. "On the other side, n is the amount of gas, counted in moles." On screen: P V = n, a cluster of dots labelled mol.

Scene 5, R. "R is the gas constant, the same number for every ideal gas: 8.314 joules per mole per kelvin. You do not work it out, you look it up." On screen: P V = n R, with R = 8.314 J mol⁻¹ K⁻¹ in a box.

Scene 6, T. "And T is temperature, which here must be in kelvin, not Celsius. To convert, add 273.15." On screen: the full PV = nRT, with a small thermometer showing 0 °C = 273.15 K.

Scene 7, the claim. "So what does it say? Keep the amount of gas and the temperature fixed, and the right-hand side is fixed. Then if pressure doubles, volume must halve. Heat the gas, and pressure, volume or both must go up." On screen: the syringe pushed in, with P growing as V shrinks.

Scene 8, the units. "Check the units. A pascal times a cubic metre is a joule. On the right, moles times joules per mole per kelvin times kelvin is also a joule. Both sides are energy, which is a good sign the equation is put together correctly." On screen: Pa × m³ = J above, mol × J mol⁻¹ K⁻¹ × K = J below, the cancelled units struck through.

Scene 9, the worked number. "One mole of gas at 0 °C and normal atmospheric pressure, 101,325 pascals. What volume does it take up? Rearrange for V: V equals nRT over P." On screen: V = nRT / P.

Scene 10, substitute. "One, times 8.314, times 273.15, all over 101,325." On screen: V = (1 × 8.314 × 273.15) / 101325.

Scene 11, the answer. "That is 0.0224 cubic metres, or 22.4 litres." On screen: V = 0.0224 m³ = 22.4 L, and a drawn box about the size of a large suitcase.

Scene 12, the check and the mistake. "22.4 litres per mole is the value in most data books, so the answer is right. The mistake almost everyone makes is leaving temperature in Celsius. Put in 0 instead of 273.15 and you get a volume of zero, which no gas has." On screen: T = 0 crossed out, T = 273.15 K circled.

Three things in that script carry over to any equation.

Each symbol gets its own scene. Scenes 2 to 6 are short, five to ten seconds each, and they are what makes the rest followable.

The unit is said with the symbol, not later. Units are where marks are lost, so they arrive at the same moment as the letter.

The mistake is shown going wrong. "Remember to use kelvin" is advice. "Put in zero and the gas vanishes" is a reason, and reasons are what viewers remember.

Revealing the equation term by term

The order you reveal the symbols matters more than how they look. A few rules:

• Left to right, as it is read. Viewers expect PV = nRT to build in the order they would say it. Jumping to T first because it is the interesting one makes the viewer hunt.
• One new symbol per beat of narration. If two symbols appear while you are still describing the first, the viewer reads ahead.
• Keep earlier symbols on screen. The equation grows. It does not replace itself. By scene 6 the viewer should see the whole thing they watched being built.
• Put the unit underneath, small. It belongs to the symbol but should not compete with it.
• Highlight, do not redraw, for the claim. When you say "if pressure doubles, volume halves", mark P and V rather than drawing a new equation. A new drawing reads as a new equation.

For longer equations, group terms and give each group a name first. The quadratic formula x = (-b ± √(b² - 4ac)) / 2a is easier as "minus b, plus or minus a square root, all over 2a", with the square root then opened up as its own scene. There is a full completing-the-square derivation of that formula in how to make a math explainer video for a class assignment; this post is about explaining an equation you already have, not proving one.

Reading symbols aloud

A voice reading symbols badly loses the viewer faster than a messy drawing. The fixes are small.

The first time a symbol appears, say its meaning in full. After that, the letter alone is fine, because the viewer now knows what it stands for. If you are using a generated voice, listen to every scene with a symbol in it. Text-to-speech can read "mol" as a word or "m³" as "m three", and those lines may need rewriting in words in the script.

When the equation has a picture

Some equations have a natural drawing, and when they do, use it. PV = nRT has the syringe. F = ma has a trolley being pushed. Ohm's law, V = IR, has a circuit with a resistor. The area of a circle, A = πr², has a circle cut into slices and laid out almost as a rectangle.

Keep the picture and the equation on screen together, and connect them. When you say "V is volume", the inside of the syringe should shade at that moment. The connection between symbol and thing is the explanation; the equation and the drawing separately are just two illustrations.

If an equation has no honest picture, do not invent a decorative one. A clean equation on a plain background beats a lightbulb.

Checklist before you export

• The question the equation answers is stated in words before any symbol appears.
• Every symbol arrives with its meaning and unit, one per scene or beat.
• The finished equation is stated as one plain sentence.
• Units on both sides are shown to match.
• One worked example with real numbers, one line of working per scene.
• The answer is compared with something known, or checked a second way.
• Every symbol, superscript, sign and unit on screen matches your working. Drawn equations get small things wrong: a missing minus, a 2 that should be a superscript, m instead of m³. Pause on each scene and check.

Make it

1. 1

   Write the question in words

   One sentence on what the equation lets you work out. If you cannot write it, look the equation up again before scripting.

2. 2

   List every symbol with meaning and unit

   A small table on paper. This becomes scenes 2 onwards, one symbol each, left to right.

3. 3

   Pick numbers for the worked example

   Choose values whose answer you can check against a data book or your teacher's notes, and write every line of working out by hand first.

4. 4

   Script the six beats

   Question, symbols, claim, units, worked number, check and mistake. Write symbols as words where they will be spoken, so the voice reads them correctly.

5. 5

   Paste the script into openCanviz

   Choose Keep my wording so the narration says the maths exactly as you checked it, set the target length, and pick whiteboard style so the equation builds the way it would on a board.

6. 6

   Check every scene against your working

   Signs, superscripts, units and the order of the lines. Fix any wrong scene in the editor, and simplify on-screen text where a line is crowded.

Common questions

How long should an equation explanation be? Two to four minutes for one equation with one worked example. At 150 spoken words a minute that is 300 to 600 words. If you need a second example, or a derivation, make it a second video.

Should I derive the equation or just explain it? Check the brief. Most exam syllabuses ask you to use an equation, not derive it, so explaining what it means and how to use it is what earns the marks. A derivation is a different video, and usually a longer one.

Can the same approach work for a chemistry equation? Partly. A balanced chemical equation is a process as much as a formula: reactants become products. Build the reactants first, then the arrow, then the products, and count atoms on both sides as the check. How to explain a process in a video covers the step-by-step side.

Is a generated voice good enough for maths and physics? Usually, provided you write symbols as words in the script. Where the brief asks for your own voice, record the narration yourself and replace the generated one. For more on the physics side, see how to make a physics explainer video that actually explains.