The Complete Guide to Unit Conversion: Methods, Exact Factors and Costly Mistakes
Most conversion errors are not arithmetic errors. They come from converting between two things that share a name but not a value: a US gallon and an imperial gallon, a “GB” that means 10⁹ bytes and a “GB” that means 2³⁰ bytes, a survey foot and an international foot. This guide shows you how to convert units correctly by hand and online, which factors are exact, and where the traps are.
It is written for students, DIY builders, cooks, travellers, freelancers who invoice in foreign currency, and anyone who needs a number they can trust.
Why conversion mistakes are expensive
Two well-documented cases show what a wrong unit costs.
- Mars Climate Orbiter (1999). NASA lost the spacecraft because ground software produced thruster data in pound-force seconds while the navigation software expected newton-seconds. NASA’s mishap investigation board named the unit mismatch as the root cause.
- Air Canada Flight 143, the “Gimli Glider” (1983). The Boeing 767 was fuelled using pounds-per-litre where kilograms-per-litre was needed. It ran out of fuel mid-flight and glided to an emergency landing. Nobody was killed.
Your own stakes are usually smaller: a kitchen shelf cut 1.6 mm short, a pressure gauge misread, a bank transfer that costs more than you expected. The method below prevents all of them.
The one method that works for every conversion
Use unit cancellation (also called dimensional analysis). Write the quantity, then multiply by a fraction that equals 1 and has the target unit on top.
Example: convert 5.5 feet to centimetres.
Start with the quantity: 5.5 ft
Use exact factors: 1 ft = 12 in, and 1 in = 2.54 cm
Arrange the fractions so unwanted units cancel:
5.5 ft × (12 in / 1 ft) × (2.54 cm / 1 in) = 167.64 cm
The ft cancels, then the in cancels, leaving cm. If the unit you want is not what remains, a fraction is upside down. This catches errors that a bare “multiply or divide?” guess never does.
Pro-tip: write the units out on paper even for simple sums. Hidden unit mistakes are usually found in the first two lines.
Converting through a base unit
Software, including the converters on this site, avoids a table of every pair by converting to a base unit first. Every length unit is stored as metres, every mass unit as kilograms, and so on. Converting inches to miles becomes inches → metres → miles. With n units, you store n factors instead of n × (n − 1) pairs, and one corrected factor fixes every pair that uses it.
Exact conversion factors worth memorising
Since 1959 the US, UK, Canada, Australia, New Zealand and South Africa have defined the yard and the pound in terms of metric units. Those definitions are exact, not rounded.
| Quantity | Exact relationship | Notes |
|---|---|---|
| Length | 1 inch = 25.4 mm | Exact by the 1959 international agreement |
| Length | 1 yard = 0.9144 m | Foot = 0.3048 m |
| Length | 1 mile = 1,609.344 m | 5,280 ft |
| Length | 1 nautical mile = 1,852 m | 1 knot = 1 nautical mile per hour |
| Mass | 1 lb = 0.45359237 kg | 1 oz = 1/16 lb ≈ 28.3495 g |
| Volume | 1 US gallon = 3.785411784 L | Imperial gallon = 4.54609 L |
| Pressure | 1 atm = 101,325 Pa | 1 bar = 100,000 Pa |
| Pressure | 1 psi ≈ 6,894.757 Pa | Derived from pound-force and inch |
| Temperature | K = °C + 273.15 | Offset, not a ratio |
| Power | 1 mechanical hp ≈ 745.7 W | Metric hp (PS) = 735.499 W |
The metre itself is defined from the speed of light: the distance light travels in 1/299,792,458 of a second (in force since 1983).
Authoritative sources for these values are the BIPM SI Brochure and NIST Special Publication 811 (Guide for the Use of the International System of Units) with NIST’s conversion tables in Appendix B.
Temperature: the one conversion that is not a ratio
Length, mass and volume scales all start at a true zero, so converting is just multiplying. Celsius and Fahrenheit zero points are arbitrary and different, so you need an offset as well as a scale.
| From → To | Formula |
|---|---|
| °C → °F | °F = °C × 9/5 + 32 |
| °F → °C | °C = (°F − 32) × 5/9 |
| °C → K | K = °C + 273.15 |
| °F → K | K = (°F − 32) × 5/9 + 273.15 |
Worked example: 98.6 °F → (98.6 − 32) × 5/9 = 66.6 × 5/9 = 37 °C.
Common pitfall: converting a temperature difference is different. A change of 10 °C is a change of 18 °F, with no +32, because the offset cancels when you subtract two readings.
Quick mental estimate: °C → °F: double it and add 30. It is accurate to within a couple of degrees between roughly 0 and 30 °C and drifts outside that range.
Look-alike units that cause real errors
| Name | Variant A | Variant B | Where it bites |
|---|---|---|---|
| Gallon | US: 3.785 L | Imperial: 4.546 L | Fuel economy (mpg) comparisons between US and UK cars |
| Cup | US customary: ≈236.6 mL | Metric: 250 mL | Recipes from different countries |
| Ton | Short ton: 907.18 kg | Metric tonne: 1,000 kg | Freight and shipping documents |
| Foot | International: 0.3048 m | US survey: ≈0.304800610 m | Land surveying, large coordinates |
| Gigabyte | SI GB: 10⁹ bytes | GiB (binary): 2³⁰ = 1,073,741,824 bytes | Storage that “shows less” than advertised |
| Horsepower | Mechanical: ≈745.7 W | Metric: ≈735.5 W | Engine spec sheets |
| Ounce | Mass (oz): 28.35 g | Fluid ounce: volume | Cooking, where mass and volume are not interchangeable |
The data-storage trap in detail
The International Electrotechnical Commission standardised binary prefixes (KiB, MiB, GiB) in the late 1990s so that “GB” could mean exactly 10⁹ bytes. Drive makers use the decimal meaning. Many operating systems historically used the binary meaning but displayed it as “GB”. That is why a “1 TB” drive shows up as about 931 “GB” in such systems. Nothing is missing: 10¹² ÷ 2³⁰ ≈ 931.3.
Pro-tip: always check which definition a tool uses. A quality converter states it on the page or uses the GiB/MiB notation for binary values.
The survey-foot caveat
The US survey foot differs from the international foot by about 2 parts per million, which is trivial for a bookshelf but over 3 cm per 10 miles. NIST and the National Geodetic Survey retired the US survey foot on 1 January 2023 for new work, recommending the international foot. If you work with older surveying data, check which foot it uses.
Currency: why it behaves differently
A physical constant never changes. An exchange rate changes every second. Four things to know:
- Mid-market rate vs the rate you get. Converters usually show a mid-market (wholesale) rate. Banks, card networks and transfer services add a margin or a fee. Treat any converter result as the reference, then compare it against the actual quote.
- Update frequency. Free data feeds often refresh once a day. That suits budgeting and price comparison, but not trading or large transfers.
- Timestamps matter. A trustworthy page tells you when the rate was last updated. Look for one.
- Rounding. Round currency to the currency’s own minor unit (two decimals for USD, none for JPY) only at the end, never in the middle of a calculation.
Scenario: a freelancer invoices 1,200 USD and wants the PKR equivalent for tax records. Use the rate for the date of the transaction, keep the source and date with the record, and do not re-run it against today’s rate later.
This site’s currency pages use ExchangeRate-API’s open data, cached for up to 12 hours. They are suitable for everyday estimates, not for trading or settlement.
Significant figures and rounding
- A conversion factor that is exact (like 25.4 mm per inch) adds no uncertainty. The precision of your answer is the precision of your measurement.
- A measurement of “5.5 ft” has two significant figures. Reporting 167.64 cm implies a precision the original never had. Write 170 cm or 168 cm, depending on how much precision you want to claim.
- Carry extra digits through multi-step calculations and round once, at the end.
- Round to match the use: 1 mm for carpentry, 0.1 mm for machining, two decimals for money.
Ten-second sanity checks
Before you trust any result, run one of these.
| Check | Example |
|---|---|
| Does the answer go in the expected direction? | A smaller unit gives a bigger number: 5 km is 5,000 m, not 0.005 m. |
| Is it in the right ballpark? | 1 mile ≈ 1.6 km, so 10 miles should be about 16 km. |
| Does the reverse give back your start? | 10 mi → 16.09 km → 10.0 mi. |
| Do units cancel on paper? | Unit cancellation (see above). |
| Is a known benchmark matched? | 0 °C = 32 °F, 100 °C = 212 °F, 1 in = 25.4 mm. |
How to choose a trustworthy converter
Use this checklist when judging any conversion tool, including ours.
- Shows the factor and formula, not just an answer, so that you can verify it.
- Names its variants (US vs imperial gallon, decimal vs binary gigabyte).
- Cites a primary source such as NIST or BIPM for fixed factors.
- Timestamps live data, and says where it came from.
- Handles temperature properly with the offset, not a bare multiplier.
- Works without sign-up and does not hide the result behind a paywall.
Trade-offs worth knowing. An online converter is fast and convenient, but it cannot warn you about a wrong input unit. Pen-and-paper unit cancellation is slower but catches that. For anything safety-critical (medication, fuel, structural loads, aviation), verify with a second method and use the unit system the governing standard specifies.
Frequently asked questions
How do I convert units quickly without a calculator?
Use rounded anchors: 1 in ≈ 2.5 cm, 1 mile ≈ 1.6 km, 1 kg ≈ 2.2 lb, 1 L ≈ 0.26 US gal. Then sanity-check against the exact figure if it matters.
Is 1 inch exactly 2.54 cm?
Yes. Since the 1959 international yard and pound agreement, 1 inch is defined as exactly 25.4 mm.
What is the formula to convert Celsius to Fahrenheit?
°F = °C × 9/5 + 32. For the reverse, °C = (°F − 32) × 5/9.
Why is a US gallon different from an imperial gallon?
They come from different historical definitions. The US gallon is 231 cubic inches (3.785411784 L). The imperial gallon is defined as 4.54609 L. The difference is about 20%.
Why does my 1 TB drive show less than 1 TB?
The manufacturer counts 1 TB as 10¹² bytes, while some software reports binary units (2⁴⁰ bytes) under the label “TB”. Divide: 10¹² / 2⁴⁰ ≈ 0.909, so about 931 “GB” per 1 “TB”.
How accurate are online currency converters?
They are accurate to the source rate they use, which is usually a mid-market rate updated at a fixed interval. Actual bank or card rates include a margin, so expect a small difference.
How do I convert a temperature change rather than a temperature?
Use only the scale factor: Δ°F = Δ°C × 9/5, with no +32 offset.
Summary and next steps
- Use unit cancellation for every conversion you do by hand.
- Memorise the exact factors (25.4 mm per inch, 0.45359237 kg per lb, 1,852 m per nautical mile) and treat the rest as derived.
- Use the offset formulas for temperature, but the scale factor only for temperature differences.
- Check which variant you are using (US/imperial, decimal/binary, mechanical/metric).
- Treat currency results as time-stamped reference rates, not quotes.
- Round at the end, and match your precision to your measurement.
Try it now: Length · Weight and mass · Temperature · Currency · Volume · Area · Speed · Time · Pressure · Angle · Power · Data storage
Popular conversions: kg to lb · cm to inches · °C to °F · bar to psi · USD to PKR · marla to sq ft
Sources
- BIPM, The International System of Units (SI Brochure), 9th edition
- NIST Special Publication 811, Guide for the Use of the International System of Units (SI), Appendix B conversion factors
- NIST Special Publication 1038, The International System of Units (SI): Conversion Factors for General Use
- NASA, Mars Climate Orbiter Mishap Investigation Board Phase I Report (November 1999)
- IEC 80000-13 / IEC 60027-2, binary prefixes (KiB, MiB, GiB)
- NIST and NOAA National Geodetic Survey notice on the retirement of the US survey foot (effective 1 January 2023)
- ExchangeRate-API Open Access documentation (data source for pakmath.com currency rates)