Online calculators save time, but they are only as good as the numbers you put in and your understanding of what comes out. Knowing the formula behind a calculator helps you spot a result that looks wrong, explain your working to someone else, and pick the right tool in the first place. This guide covers six calculators most people need at some point, with the maths behind each one and a worked example.
1. Percentage Calculations
Percentages come up everywhere: pay rises, test scores, price changes, and statistics in the news. Three formulas cover almost every situation:
- X% of Y: Y × X ÷ 100. For example, 15% of 240 = 240 × 15 ÷ 100 = 36.
- X is what percent of Y: X ÷ Y × 100. For example, 45 out of 60 = 45 ÷ 60 × 100 = 75%.
- Percentage change: (new − old) ÷ old × 100. A price rising from 80 to 92 is (92 − 80) ÷ 80 × 100 = a 15% increase.
Watch out for: percentage changes do not reverse symmetrically. A 20% drop followed by a 20% rise does not return you to where you started: 100 becomes 80, and 80 plus 20% is 96. The Percentage Calculator handles all three formulas, so you can check which one matches your question.
2. Discounts and Sale Prices
Sale price = original price × (1 − discount ÷ 100)
A jacket priced at 120 with 25% off costs 120 × 0.75 = 90, saving 30.
Stacked discounts are where people go wrong. "20% off, plus an extra 10% at checkout" is not 30% off. The second discount applies to the already-reduced price:
- 120 × 0.80 = 96
- 96 × 0.90 = 86.40
The total discount is 28%, not 30%. The Discount Calculator shows the final price and savings so you can compare offers quickly.
3. Loan Repayments
Most personal loans and mortgages use an amortising repayment, where each monthly payment is the same but the split between interest and principal changes over time. The monthly payment is:
M = P × r × (1 + r)n ÷ ((1 + r)n − 1)
where P is the amount borrowed, r is the monthly interest rate (annual rate ÷ 12), and n is the number of monthly payments.
Example: borrowing 10,000 at 6% a year over 3 years.
- r = 0.06 ÷ 12 = 0.005
- n = 3 × 12 = 36
- (1.005)36 ≈ 1.19668
- M = 10,000 × 0.005 × 1.19668 ÷ 0.19668 ≈ 304.22 per month
Over 36 months you repay about 10,951.92, so the loan costs roughly 951.92 in interest. Stretching the same loan to 5 years lowers the payment to about 193.33 but raises total interest to about 1,599.80. The Loan Calculator lets you compare terms like this side by side. Remember that real loans may also include arrangement fees, which the headline rate does not show.
4. GPA
A grade point average is a weighted average: each grade is multiplied by the credits for that course, then the total is divided by the total credits. On a common 4.0 scale:
| Course | Grade | Points | Credits | Points × Credits |
|---|---|---|---|---|
| Biology | A | 4.0 | 3 | 12.0 |
| Statistics | B | 3.0 | 4 | 12.0 |
| History | A− | 3.7 | 3 | 11.1 |
| Total | 10 | 35.1 |
GPA = 35.1 ÷ 10 = 3.51. A simple average of the three grades would give 3.57, which is wrong because it ignores that Statistics carries more credits. Grading scales differ between schools and countries, so always check your institution's scale. The GPA Calculator does the weighting for you.
5. Age
Exact age in years, months, and days requires borrowing across months of different lengths, which is where manual calculations usually slip. See our step-by-step age calculation guide for the method, or use the Age Calculator to get the answer on any reference date.
6. BMI
Body Mass Index is weight in kilograms divided by height in metres squared. A 70 kg person who is 1.75 m tall has a BMI of 70 ÷ 3.0625 = 22.9. It is a useful screening number with real limitations, which our BMI guide explains. The BMI Calculator supports both metric and imperial units.
How to Sanity-Check Any Calculator Result
- Estimate first. Round the numbers and work out a rough answer in your head. If 15% of 240 comes back as 360, you know something went wrong.
- Check the units. Monthly versus annual rates, centimetres versus metres, and pounds versus kilograms cause most wrong answers.
- Read the labels. "Interest rate" might mean APR, a flat rate, or a monthly rate. Enter the one the calculator expects.
- Watch rounding. Rounding in the middle of a calculation can shift the final answer. Keep full precision until the end.
- Know when to get professional advice. Calculators are great for comparing options, but major financial or medical decisions deserve a conversation with a qualified adviser.
Frequently Asked Questions
Are online calculators accurate?
The arithmetic is reliable when the formula is correct. Most errors come from entering the wrong value or misunderstanding what the calculator measures, which is why knowing the formula helps.
Do I need to create an account to use these calculators?
No. All ToolGhost calculators are free, work in your browser, and do not require signing up.
Why does my bank's loan figure differ from the calculator?
Banks may include fees, insurance, or a different compounding method. Ask for the APR and total amount repayable to compare like with like.