Unit Converter Calculators

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Unit conversion is the process of expressing a measurement in a different unit of the same physical quantity while preserving the underlying value. Correct unit conversion is fundamental to all quantitative science — errors in units are a common source of mistakes in laboratory calculations, clinical dosing, and engineering. The SI (International System of Units) provides a coherent system of base units (meter, kilogram, second, mole, kelvin, ampere, candela) with prefixes for powers of 10. Dimensional analysis (factor-label method) is the systematic approach to unit conversion using conversion factors.

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SI Prefixes

  • Tera (T): 10¹²
  • Giga (G): 10⁹
  • Mega (M): 10⁶
  • Kilo (k): 10³
  • Centi (c): 10⁻²
  • Milli (m): 10⁻³
  • Micro (μ): 10⁻⁶
  • Nano (n): 10⁻⁹
  • Pico (p): 10⁻¹²
  • Femto (f): 10⁻¹⁵

Dimensional Analysis

Multiply by conversion factors (fractions = 1): cancel unwanted units; target unit remains. Example: convert 55 miles/hour to meters/second: 55 mi/h × (1609 m/mi) × (1 h/3600 s) = 55 × 1609/3600 = 24.6 m/s.

Common Conversions

  • Length: 1 inch = 2.54 cm; 1 mile = 1.609 km; 1 foot = 0.3048 m
  • Mass: 1 lb = 453.6 g; 1 oz = 28.35 g; 1 kg = 2.205 lb
  • Temperature: °C = (°F − 32) × 5/9; K = °C + 273.15
  • Volume: 1 L = 0.2642 US gal; 1 fl oz = 29.57 mL
  • Pressure: 1 atm = 101,325 Pa = 760 mmHg = 14.696 psi

Glossary

Dimensional Analysis
Systematic unit conversion by multiplying by conversion factors (= 1) to cancel unwanted units; always include units in every step; the most reliable method to avoid conversion errors.
SI Prefixes
Multipliers for SI units: kilo (10³), milli (10⁻³), micro (10⁻⁶), nano (10⁻⁹), pico (10⁻¹²); essential in biology (μL, μM, ng, kDa, nm) and medicine (mg, mL, mmol/L).
Conversion Factor
A ratio of equal quantities in different units that equals 1; used in dimensional analysis; example: 1,000 mL / 1 L = 1; multiply to convert units without changing the quantity.

Frequently Asked Questions

Dimensional analysis: multiply the original value by conversion factors (each = 1 because numerator and denominator are equal quantities) chosen so that unwanted units cancel and the target unit remains. Example: convert 2.5 kg to mg: 2.5 kg × (1,000 g/1 kg) × (1,000 mg/1 g) = 2.5 × 10⁶ mg = 2,500,000 mg. Example: 0.250 L of solution → μL: 0.250 L × (1,000 mL/L) × (1,000 μL/mL) = 250,000 μL = 2.5 × 10⁵ μL. Rule: set up fractions so old units cancel: write them in the denominator of the conversion factor if they appear in the numerator of the original value.

Key SI prefixes used in science: Mega (M, 10⁶): megabase pairs (Mbp) of DNA; megapascal. Kilo (k, 10³): kilogram (kg); kilodalton (kDa); kilometer. Milli (m, 10⁻³): milliliter (mL); millimolar (mM); millisecond. Micro (μ, 10⁻⁶): microliter (μL); micromolar (μM); microgram (μg). Nano (n, 10⁻⁹): nanometer (nm, used for wavelengths and molecular sizes); nanomolar (nM). Pico (p, 10⁻¹²): picomolar (pM); picofarad. Femto (f, 10⁻¹⁵): femtoliter (fL, cell volumes); femtomolar. Order of magnitude relationships: 1 mg = 1,000 μg; 1 μL = 0.001 mL = 1,000 nL = 10⁶ pL.

Celsius to Fahrenheit: °F = (°C × 9/5) + 32. Fahrenheit to Celsius: °C = (°F − 32) × 5/9. Celsius to Kelvin: K = °C + 273.15. Kelvin to Celsius: °C = K − 273.15. Key reference points: Water freezes: 0°C = 32°F = 273.15 K. Water boils: 100°C = 212°F = 373.15 K. Body temperature: 37°C = 98.6°F = 310.15 K. Absolute zero: 0 K = −273.15°C = −459.67°F. In science: Kelvin is always used in thermodynamic equations (PV=nRT, Nernst equation, Gibbs free energy). Celsius is used for practical temperature reporting. Fahrenheit is used in the US non-scientific context.

Most frequent lab volume conversion errors: μL vs. mL confusion: 100 μL ≠ 100 mL; 100 μL = 0.1 mL. Adding 100 μL when 100 mL was needed (1,000-fold error) is a common mistake that ruins experiments. L vs. mL: 1 L = 1,000 mL; 1 mL = 0.001 L. 'μL of a 1 mM solution' vs. 'mL of a 1 mM solution': the volume unit changes the amount of solute by 1,000-fold. Solution: always write units explicitly; never abbreviate 'mL' to just 'ml'; use standard SI notation. Clinical: dosing errors frequently involve unit confusions (mg vs. μg; mL vs. L); electronic medical records and barcoding reduce these errors. Always double-check: if a calculated volume seems unreasonably large or small, recheck the unit conversion.