Science Unit Converter for School Physics and Chemistry

How to use it

Choose the quantity first — length, energy, pressure and so on — because that decides which units are offered and stops a mass being converted into a volume by accident. Then type a value, pick the unit you have and the unit you want, and set how many significant figures the answer should carry.

The answer appears twice, as a decimal and in standard form. Standard form is the one to copy into a physics answer when the number is very large or very small, because it makes the power of ten explicit rather than asking a marker to count zeros.

• Length, mass, time, area, volume, density, speed, force, energy, power, pressure, temperature and amount of substance
• Prefixes from nano (10⁻⁹) to giga (10⁹), with the ones in play highlighted
• Two to six significant figures on the answer

How the conversion is worked out

Every unit is stored as its value in the SI unit for that quantity, so a conversion is two steps rather than a lookup table of pairs: multiply by the factor for the unit you have, then divide by the factor for the unit you want. Both factors are printed above the answer with the arithmetic that produced them — 1 km/h = 1,000 ÷ 3,600 = 0.2778 m/s.

The factors are definitions rather than measurements. A litre is defined as exactly one cubic decimetre, a bar as exactly 100,000 pascals, the standard atmosphere as exactly 101,325 pascals and the international mile as exactly 1,609.344 metres. Where a factor does not terminate the displayed value carries an ellipsis, and the calculation still uses the full one.

Each unit is also written out in SI base units, so it is visible that a newton is kg·m/s² and a pascal is kg/(m·s²). That is not decoration. It is the check that tells you whether a formula has been given the right units before you trust what comes out of it.

Temperature is handled separately because it is an offset scale rather than a ratio scale. It converts through kelvin by formula — K = °C + 273.15 — and both formulas are printed instead of a factor, because no single multiplier describes the conversion.

What it deliberately does not do

It will not convert moles into grams, or a concentration into a mass. That step needs the relative formula mass of a particular substance, which belongs to the chemistry of the question rather than to the units.

It will not convert between quantities — a volume into a mass, or an energy into a power — even where the two are linked by a formula. Density and time are the missing pieces there, and slipping one in silently would produce a number that looked like a conversion but was a calculation.

It does not carry an uncertainty through the conversion, and it does not decide how many significant figures your answer deserves. That is set by the least precise measurement you started with, which is something only you can see.

Where students go wrong

Squared and cubed units are the single largest source of lost marks. 1 m² is 10,000 cm² because the factor of 100 is squared, and 1 m³ is 1,000,000 cm³ because it is cubed. Applying the length factor unchanged turns a correct method into a wrong answer.

Density is the same trap in disguise. Converting g/cm³ to kg/m³ is × 1,000, because dividing by 1,000 for the mass and by 1,000,000 for the volume leaves a net factor of 1,000. Water is 1 g/cm³, which is 1,000 kg/m³ — a useful figure to check yourself against.

Temperature catches people who are otherwise fluent. There is no factor: you add 273.15 to go from Celsius to kelvin. But a temperature difference of 5 °C is a difference of exactly 5 K, so a specific heat capacity calculation using ΔT needs no conversion at all.

• 1 m² = 10,000 cm², not 100 cm²
• 1 cm³ = 1 ml and 1 dm³ = 1 litre, exactly
• g/cm³ to kg/m³ is × 1,000
• km/h to m/s is ÷ 3.6
• K = °C + 273.15, but a change of 1 °C is a change of 1 K