Four calculators, and the formulas behind them
This page collects four calculators that share one page: a scientific calculator for expressions, a tip and bill splitter, a loan EMI estimator, and a discount calculator.
Most everyday calculation is not arithmetic — it is knowing which formula applies. Splitting a bill fairly, working out whether a sale price is actually a saving, and understanding what a loan really costs are three different problems, and only the last one is genuinely hard.
Rather than hide the maths, this page publishes the formula behind each calculator so you can check a result by hand, explain it to somebody else, or spot the moment when the tool is the wrong instrument for the decision.
The formulas used
- Scientific expressions
- Full expressions are evaluated with a mathematics parser rather than left-to-right button presses, so operator precedence, parentheses and functions behave the way they do in a textbook.
- Tip and split
- Tip = bill × percentage ÷ 100. Total = bill + tip. Each person pays the total divided by the number of people, and the tip per person is shown separately.
- Discount
- You pay = price × (1 − discount ÷ 100), and the saving is the difference. Percentages are applied to the original price, not sequentially.
- EMI
- The standard amortisation formula: EMI = P × r × (1 + r)ⁿ ÷ ((1 + r)ⁿ − 1), where P is the principal, n is the term in months, and r is the annual rate divided by 100 and then by 12.
- Zero-interest loans
- When the rate is 0, the formula above divides by zero, so the calculator falls back to principal ÷ months.
- Where it runs
- Everything is computed in your browser. No figures — salary, loan amount or otherwise — are transmitted anywhere.
Worked examples you can verify
Example 1: Splitting a restaurant bill
Bill: 84.00
Tip: 15%
People: 3Tip: 12.60
Total: 96.60
Each person: 32.20
Tip per person: 4.20The tip is calculated on the pre-split total, which is the fair method. Splitting first and tipping individually produces rounding differences and awkward conversations.
Example 2: What a loan actually costs
Principal: 100,000
Annual rate: 10.5%
Term: 60 monthsMonthly EMI: 2,149.39
Total repayment: 128,963
Total interest: 28,963The interest figure is the number worth looking at. Extending the same loan to 84 months lowers the monthly payment and raises the total interest substantially — the trade-off that loan advertising rarely puts side by side.
Example 3: A discount that is smaller than it looks
Original: 2,400
Discount: 30%You pay: 1,680
You save: 720Stacked offers do not add. A 30% discount followed by a further 20% off the reduced price gives 44% off in total, not 50% — each percentage applies to a smaller base.
Where these estimates stop being reliable
Direct answer: the EMI figure is a mathematically correct amortisation payment. It is not a quote, and real loans carry costs this formula does not contain.
Fees are not included
Processing fees, insurance bundled into the loan, documentation charges and prepayment penalties all change the true cost. The comparable figure across lenders is the APR, not the headline rate.
Only fixed-rate loans behave this way
A floating-rate loan reprices during the term. The payment or the number of instalments will change, and the total interest with it.
Rounding differs between lenders
Banks round instalments to whole currency units and adjust the final payment. Expect small differences between this estimate and a lender’s schedule; a large difference means an assumption is wrong.
Tipping norms are cultural, not mathematical
Fifteen to twenty percent is a North American convention. Elsewhere a service charge may already be included, or tipping may not be customary at all. The calculator applies whatever percentage you give it.
Tax and service charge order matters
Tipping on the post-tax total is a different amount from tipping on the subtotal. Decide which you intend before entering the bill.
Not financial advice
These are arithmetic tools. Whether a loan is affordable depends on income stability, existing obligations and risk tolerance — none of which appear in the formula.
Getting more out of these calculators
- Compare loans by total interest, not monthly payment — a lower instalment over a longer term almost always costs more.
- Run the EMI twice, with and without a lump-sum prepayment in mind, to see how much interest an early payment saves.
- For a group bill, agree whether the tip applies before or after tax before the plates are cleared.
- When comparing sale prices, calculate the final amount for each option rather than comparing discount percentages.
- Working out someone’s exact age for a form or an eligibility rule? Use the age calculator instead of counting months by hand.
How this page is maintained
The tip, discount and EMI formulas above — including the zero-interest fallback — were read from this page’s implementation, and the worked examples were produced by the calculators themselves. Results are described as estimates because real loans include costs no payment formula captures.
Written and reviewed by the ToolsRacks editorial team. Last reviewed: .