True Value Calc brings together 583 free online calculators, converters, practical utilities, and research-backed articles covering finance, health, mathematics, science, and everyday needs — created and maintained by a researcher who holds a PhD, with a focus on accuracy, transparent methodology, trusted sources, and clear explanations that help users understand formulas, concepts, and results and make informed decisions with confidence.
Right arithmetic and the right answer are not the same thing — a tool can be flawless at one and useless at the other. Every calculator here shows its working so the result can be checked rather than trusted, and six things decide whether a number means what you think it means.
See it done on a real mortgage → How these tools are built & checked →
Try a different keyword — e.g. "mortgage", "tax", "BMI", "loan", or "retirement".
Longer pieces on the research behind everyday financial questions — what the published literature actually measured, where it contradicts the rule of thumb everyone repeats, and where the model stops applying. Written from primary sources by Dr Sam. See our full methodology →
The post-2008 transformation of the U.S. mortgage market produced a difficult trade-off. This article examines that tension between financial stability and access to homeownership.
Mortgage Calculator →The economic effectiveness of a defined-contribution retirement plan cannot be inferred from participation rates or account balances alone.
401k Calculator →8×8 is not established as a universal individual requirement. Water turnover varies substantially between people based on body mass, environment, and physical activity.
Water Intake Calculator →Every tool on this site shows its working. These are not claims about the calculators — they are things you can check on the page itself.
Most web calculators work as black boxes: a number goes in, an opaque figure comes out, and nothing on the page says which tax bracket was applied, how the amortisation decays, or which statutory rule the answer depends on. This site is built the other way round — the working is part of the output, so a result can be checked rather than taken on faith.
Everything here is provided for information and planning. These tools are not financial, medical, tax or legal advice, and results should not be the sole basis for a significant decision. For anything material — a mortgage application, a tax filing, a change in medication or diet — the numbers here are a starting point for a conversation with a qualified professional, not a replacement for one.
How we build & check these tools → Research Articles → Who builds them →
A calculator can give you the right arithmetic and still give you the wrong answer for the decision you are trying to make.
That distinction is the reason this site exists. True Value Calc brings together calculators, converters, reference charts and analytical models for finance, mathematics, science, health, measurement, time and everyday decisions. The library is large, but its size is not the point. The purpose is to make the calculation itself understandable: what is being calculated, which formula produces it, what assumptions are built into the result, which external data it depends on, and where it stops being reliable.
A mortgage payment can be calculated to the cent and still be an incomplete picture of what owning a home costs. A fuel-economy conversion can be flawless and still be wrong if a US gallon has been read as an imperial one. A paycheck estimate can apply a federal tax calculation correctly and still land a long way from someone's actual take-home pay, because state tax, benefits and filing circumstances were never part of the model.
A useful calculation should expose the reasoning that produced the result, rather than presenting the result as an unexplained fact.
In practice that means showing, where they apply, the formula, the inputs, the assumptions, a worked example, the source data and the limits of what the tool can tell you. The rest of this page is that principle applied — starting with an actual calculation rather than a description of one.
Take the most common question on the site: what does a $400,000 mortgage at 6.5% over 30 years cost per month? Here is the whole calculation, not just the answer.
M = P × [ i(1 + i)^n ] ÷ [ (1 + i)^n − 1 ]M = 400000 × [ 0.00541667 × 6.991798 ] ÷ [ 6.991798 − 1 ]Monthly principal and interest: $2,528.27
Over the full term that is $910,177.95 paid on a $400,000 loan — $510,177.95 of it interest. And the first payment is not split the way most people expect: of that $2,528.27, $2,166.67 is interest and only $361.61 reduces the balance. That single figure explains more about early-years mortgage behaviour than any summary sentence could.
$2,528.27 is the scheduled debt service. It is not what the house costs to live in. Add property tax and homeowners insurance and the monthly figure moves substantially:
2528.27 (P&I) + 366.67 (tax) + 166.67 (insurance) = $3,061.61 per monthAssumptions in that second figure, stated rather than buried: property tax at 1.1% and insurance at 0.5% of value per year. Both are illustrative only. Effective property-tax rates vary by more than a factor of five between US states and vary again by county, and insurance depends on the property, the deductible and the risk profile of the location. Neither is a national constant, and any tool that treats them as one is quietly guessing on your behalf. Mortgage insurance, HOA charges and maintenance are excluded here and can each move the total again.
So the same house produces two defensible monthly numbers — $2,528.27 and $3,061.61 — that differ by 21%. Neither is wrong. They answer different questions, and knowing which one a calculator gave you is the difference between a budget that works and one that does not.
It is widely assumed that two calculators fed the same figures should return the same number. That is not necessarily true, and neither of them has to be broken for it to happen. Two tools can follow different conventions while each performs its stated mathematics correctly.
The difference commonly comes from monthly versus daily compounding; nominal versus effective interest rates; contributions applied at the beginning rather than the end of a period; different payment dates; different rounding conventions; different definitions of the same unit; different inflation datasets; different tax years; different treatment of fees; different assumptions about insurance, taxes or other recurring costs; or different rules for partial periods and leap years.
The mortgage above is the plainest case: one calculator returns principal and interest, another folds in taxes, insurance and fees. The two figures are not contradictory. They are answers to different questions.
Before comparing two answers, compare what each calculator is actually calculating. A difference of a few cents is usually rounding. A difference of hundreds is usually a missing cost, a different interest convention, a different tax assumption, or a fundamentally different model.
A result you can rely on has more than one layer behind it, and a tool can be correct at one layer while being useless at another.
Define exactly what is being measured. "Monthly payment" is not "total monthly housing cost", as the example above shows. "Return" is not "annualised return". "Income tax" is not "total payroll deductions". "Volume" is not interchangeable with "mass". Precision begins with definition, not with decimal places.
The inputs have to describe compatible quantities. A field labelled "gallon" is not sufficient when more than one gallon exists. A weight entered in pounds cannot be silently treated as kilograms. Unit errors are particularly dangerous because the number that comes out still looks entirely reasonable.
The mathematical relationship should be identifiable and printed, as it is above. A formula tells you how the parts interact; it does not tell you whether the parts are the ones your decision depends on. That distinction between a mathematical calculation and a real-world model is the one most often lost.
Some calculations are almost purely mathematical. Others depend on information that changes: tax thresholds for a given year, contribution limits, a price index, a published dataset and its date. For those tools the source and the applicable period are part of the calculation, not a citation added afterwards.
Every model leaves something outside its boundary. An investment projection may assume a constant rate of return. A calorie estimate uses a published predictive equation rather than a measurement of one person's metabolism. A depreciation figure follows a particular convention. A calculator becomes more useful the moment those assumptions are visible rather than embedded.
A result should not imply more certainty than the model can carry. A unit conversion is exact within the precision of its conversion factor. A thirty-year projection is a different kind of object entirely: a scenario built on assumptions about contributions, returns, inflation, fees, taxes and time. The decimal places are precise. The future is not.
The English-speaking world shares a language but not a measurement system, a tax system or a set of financial structures. That matters the moment a calculation crosses a border, and it accounts for a whole class of wrong answers that look completely plausible.
A US liquid gallon is roughly 3.785 litres. An imperial gallon is roughly 4.546 litres, about twenty per cent larger. A vehicle described as achieving 40 miles per imperial gallon is doing about 33.3 miles per US gallon — the same car, described two ways. The arithmetic is trivial; the mistake happens before the arithmetic begins, when the same word is assumed to mean the same volume everywhere. Litres per 100 kilometres, used in Canada and Australia, adds a further reversal: on that scale a lower number is better. A unit label is part of the data.
Canada adopted the metric system decades ago, yet Canadians still commonly give body weight in pounds and height in feet and inches. The United Kingdom measures body weight in stones and pounds, where one stone is fourteen pounds, so eleven stone four is 158 pounds or about 72 kilograms. Australia is consistently metric; the United States is consistently imperial. A body mass index calculation is arithmetically identical everywhere, but the units people reach for are not.
A cup measures volume, a gram measures mass, and the relationship between them depends on density:
mass = volume × densityA US cup is about 237 millilitres; an Australian metric cup is 250; modern British recipes usually give weights in grams and skip cups altogether. Because flour, sugar and butter have different densities, a cup of one is not interchangeable by weight with a cup of another — and even within one ingredient, packing and particle size move the result. A cups-to-grams conversion that offers a single universal factor is not simplifying the problem; it is hiding it.
Measurement differences are inconvenient. Financial differences are more consequential, because the structure of a product — not just its price — changes from one country to the next.
The interest rate is locked for the full term of the loan. Retirement saving runs through 401(k) plans and IRAs, and income is taxed at both federal and, in most states, state level.
Mortgages typically fix for a five-year term but amortise over twenty-five years, so borrowers renegotiate repeatedly over the life of the loan. Retirement saving centres on RRSPs and TFSAs.
Fixed periods of two or five years are common, after which the loan usually reverts to a lender's standard variable rate. Tax-advantaged saving happens through ISAs and workplace pensions.
Variable-rate mortgages are widespread, and offset accounts are a familiar feature. Retirement saving is dominated by the compulsory superannuation system.
The practical consequence is that the $2,528.27 calculated above holds for thirty years only under US conventions. Model a Canadian or British loan with the same formula and the figure is honest only for the length of the current fixed period; beyond it the rate is unknown, and the projection becomes a scenario rather than a forecast. Re-running it at a higher rate to see what the payment becomes is more informative than trusting the original number.
Financial mathematics is unusually vulnerable to false precision, because a clean formula can conceal every cost and assumption sitting outside it. Three cases come up constantly.
A lower interest rate does not automatically make refinancing worthwhile, because the new loan carries closing and origination costs that have to be recovered first:
break-even period = refinancing costs ÷ monthly savingEven that has limits. A full comparison also has to weigh the new term, the remaining balance, prepayment penalties where they apply, points and fees, the change in total interest over the whole horizon, and how long the borrower actually expects to keep the loan. The useful question is not "is the new rate lower?" but "does the benefit justify the cost, and the time needed to recover it?"
Gross salary is a stated compensation figure, not the amount available to spend. Between the two sit federal income tax, payroll taxes, state or local taxation, retirement contributions, health benefits and other deductions. In a progressive system, moving into a higher marginal bracket does not mean the whole salary is taxed at that rate — only the portion above the threshold is. The figure that describes the overall burden is the effective rate:
effective tax rate = total tax ÷ relevant income baseWhat counts as the denominator depends on the calculation, which is exactly why a paycheck model should state its tax year, jurisdiction, filing assumptions and included deductions. People compare job offers using gross salary when the thing they actually care about is disposable income.
For a starting balance, a regular contribution, a periodic return r and t periods, a simplified future value is:
FV = P × (1 + r)^t + PMT × [ ((1 + r)^t − 1) ÷ r ]where P is the opening balance and PMT is the contribution made each period.
The formula is exact for the assumptions it describes; the assumptions are not guaranteed. Real outcomes differ because returns vary from year to year, contributions change, inflation erodes purchasing power, fees and taxes reduce net growth, and the order in which returns arrive matters a great deal once money is being withdrawn. The balance between contributions and returns also differs from person to person — there is no universal crossover point at which compounding "takes over", which is why a projection is worth more when you can change its assumptions than when it hands you one impressive number.
Instead of asking what will my money be worth in twenty years?, ask how much does the answer move when the assumptions move? Run the same model three times.
| Scenario | Contribution | Return assumption | What the run is for |
|---|---|---|---|
| Conservative | Minimum you are confident of sustaining | Lower bound — a stressed return | Stress test. Does the plan still work through an extended downturn, or does it depend on nothing going wrong? |
| Base | Target contribution | Central assumption | Operating case. The version you actually plan around and review against. |
| Optimistic | Upper end of what you could save | Favourable return band | Upside reference. Shows what is possible without making it a prerequisite. |
The specific figures belong to the model in front of you rather than being universal constants. What the exercise reveals is sensitivity: if a plan only works under one unusually favourable assumption, that is important information in itself, and it is exactly what a single headline number hides.
Not every calculator can be used everywhere, and it is worth being direct about that rather than implying more coverage than exists.
Length, area and volume; temperature; geometry; basic statistics; arithmetic and mathematical functions; calendar and date calculations; physical unit relationships. The mathematics does not change because you crossed a border. The definitions of the inputs still do, which is what the gallon and the cup are about.
Loan amortisation, compound growth, future and present value, internal rate of return, net present value, depreciation, debt repayment comparisons. The mathematics travels; the surrounding rules may not. A pre-tax amortisation formula is universal, while the tax treatment of interest, fees, deductions or investment income is jurisdiction-specific.
Federal income tax, FICA, state taxation, retirement-account contribution limits, IRS thresholds and deductions, and payroll withholding. These are tied to one legal system and should not be read as applying elsewhere. A US paycheck calculator is not a Canadian T4, UK PAYE or Australian PAYG calculator merely because "take-home pay" means something similar in each. Outside the US, use these tools for the underlying arithmetic — gross to net at a given rate, or the effect of a pension contribution on taxable income — and apply your own country's rates.
Scope is part of accuracy. A tool that quietly implies universal applicability is wrong in a way that is much harder to notice than an arithmetic error.
Different calculations rest on different evidence. A physical conversion depends on a standardised unit definition. A financial calculation depends on a mathematical identity plus current statutory or economic data. A health estimate depends on a published predictive equation. A tax tool depends on legislation and filing rules for a particular year. Those are not interchangeable sources, and treating them as one category is how a page ends up citing an agency for something the agency never said.
So it is worth separating the formula that performs the calculation from the external information the formula consumes. A formula does not become incorrect when a tax threshold changes; the implementation simply needs the current input. In the other direction, a historical inflation calculation should use the dataset for the period selected rather than silently substituting today's value. Where a tool depends on figures that move, the year those figures apply to is stated alongside them, so an ageing number is visible rather than silent. The fuller account of how these tools are built, checked and corrected is on the methodology page.
The calculators here run in your browser rather than on a server, so figures you type produce a result immediately, without an account, a sign-up or a submitted form. That matters most where the inputs are personal — a salary, a loan balance, a body weight — because the calculation never requires handing those figures over.
Two honest exceptions are worth stating plainly. First, tools that display a current mortgage rate or exchange rate have to retrieve that public figure from an outside source; those requests bring a published benchmark back to the page and carry nothing you entered. Second, this site uses analytics, which records that a tool was used and on which page — never the values in the fields. The principle is simply: compute locally where the calculation can be local, and name the external dependency where one genuinely exists.
A result printed to two decimal places creates an illusion of certainty. "$2,528.27" is meaningful to the cent only inside the model that produced it, and "investment value after 30 years: $1,247,381" does not mean an account will hold that amount. It means: if the stated assumptions hold, this model produces that result.
Which is why a good tool also tells you when not to use it. A mathematical calculator is entirely suitable for a well-posed numerical problem. A financial calculator is useful for comparing scenarios and poor at predicting the future. A health calculator returns an estimate from a published formula without diagnosing anybody. A tax calculator illustrates an estimated liability without replacing a filing or professional advice. Exact arithmetic does not produce an exact real-world conclusion — so assumptions and limitations are treated here as part of the result rather than as small print beneath it.
That is the whole standard, and it is deliberately unglamorous: define the problem, use the right units, show the formula, name the external data, state the assumptions, test the calculation, explain the limits, correct errors in the open, and wherever practical let you change the assumptions and watch the answer respond. A calculator can remove arithmetic work and make a formula legible. It cannot remove uncertainty from the world. The most useful result is not the one with the most decimal places — it is the one whose reasoning you can see.
The collection is broad because everyday calculations are broad. The methodology is what keeps individual tools from turning into unexplained answer boxes.
True Value Calc provides calculators, converters, reference information and scenario models for educational, informational and planning purposes. Results depend on the values you enter, the assumptions each model applies, the data sources it draws on, the dates those sources apply to, rounding conventions, and jurisdiction-specific rules that may not match your own.
Financial, tax, legal, medical, fitness and other professional decisions frequently depend on information that a general-purpose calculator cannot capture. Nothing here should be treated as a substitute for advice from an appropriately qualified professional, or for official documents and regulatory guidance.