How to build a formula sheet from engineering PDF notes

Why a formula sheet is more than a list to memorise

In engineering courses there is a big gap between knowing a formula and using it correctly. Even if you remember the equation in the exam, using the wrong unit, the wrong temperature scale or a case where it does not apply still gives you the wrong answer. A sheet that only lists equations one under another does not prevent those mistakes; it does not tell you what to check as you read it.

A good formula sheet puts four things next to each equation: what the symbols mean, which units they take, when the formula is valid, and the mistake people make most often. This guide applies those four columns to the ideal gas equation from thermodynamics. For studying a whole set of lecture notes, see the engineering lecture notes guide; this page focuses only on the formula sheet and on revising formulas.

Ask your instructor whether a formula sheet is allowed in the exam, what size it can be and whether it has to be handwritten. Even if it is not allowed, writing one is good revision: as you fill it in, you notice which conditions you do not know.

Build the sheet in four columns

1. Write the formula and its symbols. Define each symbol exactly as your lecture notes do. The same letter can stand for different quantities in different courses.
2. Add the units. Write the unit you are working in next to each symbol. Do not forget the units of constants: a constant's value only means something together with its unit.
3. State when it applies. Conditions such as “closed system”, “constant mass” or “ideal gas assumption” matter as much as the formula itself. If you cannot find the condition in your notes, look for it in the lecture or the textbook.
4. Note the common mistake. Add the mistakes you make in practice problems to this column. Over time the sheet shows not just the formulas but your own pitfalls.

Do not write the sheet once at the start of term and leave it. Each week, as you add the new topic's formulas, go back over the older rows and remove anything that repeats.

Example: the ideal gas equation row

This section is an example. The source paragraph, table, calculation, question and cards were written for this guide for teaching purposes. They are not taken from a student's upload or from a live LectureSift output; check the constants and conditions against your own lecture notes.

Source paragraph

The ideal gas equation is written PV = mRT, where P is absolute pressure (kPa), V is volume (m³), m is mass (kg), R is the gas constant of the gas and T is absolute temperature (K). For air, R = 0.287 kJ/(kg·K). Gases behave as ideal gases at low pressure and high temperature relative to their critical point. Close to a phase change, for example in the saturated vapour region, property tables should be used instead of the ideal gas equation.

Formula sheet rows

Unit check: 1 kPa·m³ = 1 kJ. So in mRT/V the kg and K cancel, leaving kJ/m³, and kJ/m³ is the same as kPa. If the units do not cancel, check your symbols again before starting the calculation.

Worked calculation

A piston–cylinder device holds 2 kg of air in a volume of 1 m³ at 27 °C. What is the pressure?

1. Convert the temperature to kelvin: 27 + 273.15 ≈ 300 K.
2. Rearrange for pressure: P = mRT/V.
3. Substitute: P = 2 × 0.287 × 300 / 1 = 172.2 kPa.

Had the temperature been entered as 27, in degrees Celsius, the result would have been 15.5 kPa, more than ten times too small. Asking whether the answer is plausible helps you catch that kind of mistake.

Question

The same air is compressed to 0.5 m³ while its temperature is held constant. What is the final pressure in kPa? A) 86.1 · B) 172.2 · C) 344.4 · D) 688.8

Flashcards

Taking formulas from PDF notes

• Check subscripts and powers. In formulas copied from a PDF or read with OCR, P₁ can come out as “P1” and m³ as “m3”, and the structure of fractions and roots can break. Compare each formula with the original page before you move it to your sheet.
• Write constants with their units. The value 0.287 for R holds in kJ/(kg·K). If the unit changes, so does the number.
• Mark the cases that need tables. Also write on the sheet where the formula is not enough and you have to go to a property table.
• Test the sheet on problems. Work through a few problems using only the sheet. If you notice a missing condition or unit, fix the row straight away.

For steps to compare AI output with its source, see the guide to checking notes made from a PDF.

Using LectureSift to revise formulas

When you upload your lecture notes as PDF, DOCX, PPTX or TXT, LectureSift prepares a summary and smart notes, quiz questions with explanations, and flashcards. Scanned pages without a text layer are read with OCR. You can also upload a lecture recording as MP4, MP3, WAV or MOV; for video, the “Slide images” option tries to capture the presentation pages shown on screen during the lecture. You can check formulas against those images too, but there is no guarantee every screen will be captured.

LectureSift does not make a formula sheet for you. You move the formulas from the summary and notes into the four columns above yourself. That transfer makes you think about each formula's condition and units, so it is part of the revision. Use the quiz questions to test your sheet, and rework any numerical answer yourself before accepting it. On a free account you can download the study pack as a PDF; Word and TXT exports are on paid plans.

Frequently asked questions

Try it with your own notes

Create a free account · Plans and allowances