How to

Put numbers in front of each formula until every element has the same count on both sides. A method you can do by hand, a worked aluminium example and a mass check.

Lay out a 2 × 2 table, multiply across the diagonals (ad ÷ bc), then build the interval on the log scale. A worked case-control example, and how to read the answer.

Divide weight in kilograms by height in metres squared. A worked example in metric and US units, the WHO adult bands, and what BMI cannot tell you.

Work out the doubling time of a cell culture from two or more counts, using the log-linear fit, and spot the lag phase that throws it off.

Grow the start amount by (1 + r/m)^(m×t), add the growth of each regular deposit, and subtract what you paid in to get the interest. Worked example and checks.

Estimate resting energy (BMR) from weight, height and age, then multiply by an activity factor. A worked example with four equations and honest limits.

Turn an A260 reading into ng/µL, check purity with 260/280 and 260/230, and get nM, copies per µL and a dilution, with a worked plasmid example.

Divide the distance by your fuel economy to get the fuel used, then multiply by the price. Worked US and metric road-trip examples, split between passengers.

Amount left = start × (1/2)^(t ÷ half-life). How to use it both ways, a worked iodine-131 example, finding a half-life from two readings, and quick checks.

Take the new value minus the old one, divide by the old value and multiply by 100. A worked pay-rise example, quick checks and the common traps.

Work out a PCR primer's Tm from its GC content, compare three simple formulas and pick a starting annealing temperature, with a worked primer pair.

Add resistors in series; add the reciprocals for resistors in parallel. A worked 9 V circuit with the total resistance, the current in every branch and quick checks.

Work out how many survey responses you need for a chosen margin of error and confidence level, with the small-population correction and a worked example.

Find the mean, square each distance from it, average the squares and take the square root. A worked example by hand and with a live tool, plus the n − 1 sample version.

Multiply the appliance's watts by the hours it runs, divide by 1,000 to get kWh, then multiply by your price per kWh. A space heater and a computer worked through.

Split the launch speed into sideways and upward parts, find the time in the air, then multiply by the sideways speed. Formula, worked example and quick checks.

An APA 7 web page reference is author, date, title in italics, site name and link. Here is the pattern, a worked example and what to do with no author or no date.

Divide the mass in grams by the molar mass in g/mol. How to find the molar mass from a formula, a worked baking soda example, and quick checks.

Multiply your hourly rate by hours a week, then by the weeks you are paid in a year. A worked example with unpaid leave and overtime, plus quick checks.

Count live and dead cells in a Neubauer chamber, turn the tally into cells per mL and viability, then work out the volumes to seed a plate.

Multiply the concentration you want by the volume you want, divide by the stock's strength, and that is how much stock to take. Worked example and checks.

Put your counts in a table, work out the count you would expect in each cell if the two variables were unrelated, add up (O − E)²/E and read the p-value. Worked example included.

Write each parent's gametes along two sides of a grid, fill every box, then count. A worked tall and short pea plant cross, the 3 : 1 and 1 : 2 : 1 ratios, and how to check them.

Paste two columns of numbers, let the tool pick Welch's or Student's t-test, then read t, the degrees of freedom, the p-value, the confidence interval and Cohen's d.

Label the sides from the angle you know, pick the ratio that links the side you have to the side you want, then multiply or divide. Worked ladder example and checks.

Count the outcomes in each region of the Venn diagram, then divide by the total: P(A ∪ B) = P(A) + P(B) − P(A ∩ B). Worked example, a survey shortcut and checks.

Find where the curves cross, take the top curve minus the bottom one, and integrate between the crossing points. Worked example with y = x + 2 and y = x², plus checks.

Enter your place and date, then read when each planet rises, when it is highest and how bright it is. A worked example for Delhi and quick ways to check what you see.

Fit y = a·exp(−x/t) + c to measured data by least squares, read the time constant with its uncertainty, and check the fit with residuals and chi-square.

Pick a buffer whose pKa is close to your pH, work out the acid-to-base ratio, weigh the two forms and check with a pH meter. A worked acetate example.

List each subject's time and whether the event happened, then multiply the survival fraction down at every event time. A worked example by hand, the log-rank test, and what censoring means.

Multiply the molarity by the volume in litres and the molar mass to get the grams to weigh. A worked example with a hydrate, and how to check it.

Use one column, plain headings, dates for every job and the job ad's own words. Check it with a free ATS score out of 100, worked through on an example resume.

Pay a little more than your monthly payment, or add lump sums, so the balance falls sooner. See the interest saved and the new end date, with a worked example.

Combine the uncertainties of your measurements into the uncertainty of a calculated result, the GUM way, with a kinetic energy example and a Monte Carlo check.

Turn the bands into digits, add the multiplier's zeros, then read the tolerance band. Worked 4-band and 5-band examples, plus how to tell which end to start from.

Turn on Fit an upload limit, pick the size the portal allows, and the PDF is shrunk on your own device. The maths of DPI and page images, with a worked example.

Make the photo fewer pixels wide first, then let the quality drop just enough to fit the KB limit. Steps, the maths behind it and a worked example.

Find the discriminant b² − 4ac, then use x = (−b ± √D) / 2a, or split the middle term when the roots are whole numbers or fractions. Worked example and checks.

Put the object distance and focal length into 1/v − 1/u = 1/f with the right signs, solve for v, then get magnification and power. Worked example and checks.