Numerical Reasoning Formulas Cheat Sheet: Every Formula You Need (2026)

Numerical reasoning tests are rarely about difficult mathematics. They test whether you can extract the right figures from a table or chart, choose the correct calculation, and execute it accurately under time pressure. Most of the maths needed is taught by age 16, which is exactly why a compact formula sheet is so effective: it removes the hesitation of working out the method while the clock runs.

The full format varies by publisher. A commonly reported SHL Verify numerical test gives around 25 minutes for roughly 18 questions, which is about 80 seconds per item once you account for reading time. Our main numerical reasoning guide covers the test structure; this page is the quick-reference companion for the calculations themselves.

The 12 formulas at a glance

Percentages appear in almost every numerical reasoning test, usually combined with a table. Four variations cover nearly everything you will meet.

1. Percentage of a number

Multiply by the percentage and divide by 100. Shortcuts: 10% is the number divided by 10; 5% is half of that; 1% is the number divided by 100. So 15% of 240 is 24 + 12 = 36.

2. Percentage change

(New − Old) ÷ Old × 100. Revenue moving from £4.2m to £4.83m is (0.63 ÷ 4.2) × 100 = 15% growth. Always divide by the starting value.

3. Reverse percentages

When you are given the final figure and the rate, divide by the multiplier. After a 20% increase the multiplier is 1.20; after a 20% discount it is 0.80. A jacket sold at £60 after 20% off was originally £60 ÷ 0.80 = £75.

4. Successive percentages

Multiply the multipliers. A 10% rise followed by a 10% fall is 1.10 × 0.90 = 0.99, a net 1% fall, not zero. Similarly, 20% of 30% is 0.2 × 0.3 = 6%.

Percentage formulas side by side

Ratio questions describe how a quantity is split, or ask you to scale a recipe, budget or workforce. The method is always the same: add the parts, find the value of one part, then multiply.

Worked example: A £400 budget is divided between three teams in the ratio 3:5:2. The parts sum to 10, so one part is £40. The teams receive £120, £200 and £80. Check by adding: 120 + 200 + 80 = 400.

Direct proportion: if 6 units cost £45, 10 units cost 45 ÷ 6 × 10 = £75. Inverse proportion: if 4 people finish a task in 9 days, 6 people need 4 × 9 ÷ 6 = 6 days.

Fractions worth memorising as percentages

The mean is the total divided by the number of items. When the question gives you the mean and the count, work backwards: total = mean × count. This is especially useful for “what must the next score be to reach an average of…” problems. If five scores average 72, the total is 360; to reach an average of 75 across six scores you need 450, so the sixth score must be 90.

Weighted averages: multiply each value by its weight, add, and divide by the total weight. A product line with 60 units at £10 and 40 units at £15 has an average price of (600 + 600) ÷ 100 = £12.

Speed, distance and time: distance = speed × time. A journey of 90 km taking 1 hour 30 minutes is 90 ÷ 1.5 = 60 km/h. Convert minutes to decimals before dividing (30 minutes = 0.5 hours).

Rates: “per unit” problems such as output per hour or cost per mile are simple division. Work out the unit rate first, then scale.

Currency questions give an exchange rate and ask you to convert a value, sometimes through two steps. If £1 = $1.25, then £80 = 80 × 1.25 = $100, and $150 = 150 ÷ 1.25 = £120. The rule is: multiply when moving into the currency that has the larger number per pound, and divide when coming back.

When two conversions are chained, for example pounds to euros to dollars, convert one step at a time and keep a note of each intermediate result. Do not shortcut by averaging rates.

Unit conversions follow the same logic: 1 km = 1,000 m, 1 hour = 60 minutes, 1 tonne = 1,000 kg. Watch for charts labelled “£ thousands” or “$m” — the unit in the title often changes the final answer by a factor of 1,000.

Employers in finance, consulting and retail rely on business-flavoured questions, so know these cold. See also our guide to investment banking aptitude tests, where these formulas are tested most heavily.

Margin versus mark-up

Margin is profit as a share of selling price; mark-up is profit as a share of cost. A product costing £80 and selling for £100 has profit of £20, a 20% margin (20 ÷ 100) but a 25% mark-up (20 ÷ 80).

Sales tax and VAT

To add UK VAT at the standard 20% rate, multiply by 1.20. To strip it out of a VAT-inclusive price, divide by 1.20: £120 including VAT is £100 before VAT.

Simple and compound interest

Simple interest = principal × rate × years. Compound growth = principal × (1 + rate)ⁿ. £1,000 at 5% compounded annually becomes £1,050 after one year, £1,102.50 after two and £1,157.63 after three.

Growth rates and index numbers

An index sets a base year to 100. If the index is 130 in 2023 against 100 in 2019, the measure rose 30% over the period. Compound annual growth rate (CAGR) is (end ÷ start)^(1 ÷ years) − 1: growth from 100 to 144 over two years is √1.44 − 1 = 20% a year.

Knowing the formula is only half the skill. In the real test the numbers sit in a table, bar chart or line graph, and the question wording tells you which formula to use. Follow a consistent routine:

• Read the question first — decide what is being asked before you look for data.
• Check titles, units and time periods on the table or chart.
• Identify the two numbers you need and write them down.
• Choose the formula from your sheet and compute.
• Sense-check the answer against the chart: a 40% rise should look like roughly a 40% taller bar.

Multi-step questions often combine two formulas, such as “what is the average annual percentage growth in sales between 2021 and 2024?” Break them into a first calculation (total or change) and a second (average or percentage), writing the intermediate result down. For the other test components that sit alongside this one, read our ultimate guide to aptitude tests.

Time, not difficulty, is what causes most candidates to underperform. Three habits make the biggest difference.

• Budget your time. If a question has taken more than about 90 seconds, flag it, guess, and move on — unanswered questions score nothing.
• Round smartly. Round 4,872 to 4,900 for estimates; only calculate exact values when the answer options are close together.
• Use the calculator for multi-digit arithmetic only. Mental maths is faster for 10%, 50% or simple fractions.
• Keep rough paper tidy. Label intermediate figures so you can re-check without recalculating.

Scores are normally compared with a norm group, so accuracy plus speed both matter. Our guide to what is a good SHL score explains how raw marks convert to percentiles, and SHL Verify Interactive describes the adaptive format used in some assessments.

For harder, data-heavy items, move on to the numerical critical reasoning guide, and if your employer uses the Korn Ferry or Cut-e brand, see Korn Ferry Talent Q for how its numerical sections differ.