StudySmarter - The all-in-one study app.

4.8 • +11k Ratings

More than 3 Million Downloads

Free

Suggested languages for you:

Americas

Europe

Converting Units

To be able to convert from one type of unit to another, we need to know the equivalence between both units. We can convert between units as long as both use the same basic units because they must measure the same physical property.Consistency is needed when converting units. We cannot convert time to length, but we can translate time to frequency because…

Content verified by subject matter experts

Free StudySmarter App with over 20 million students

Explore our app and discover over 50 million learning materials for free.

Converting Units

- Astrophysics
- Absolute Magnitude
- Astronomical Objects
- Astronomical Telescopes
- Black Body Radiation
- Classification by Luminosity
- Classification of Stars
- Cosmology
- Doppler Effect
- Exoplanet Detection
- Hertzsprung-Russell Diagrams
- Hubble's Law
- Large Diameter Telescopes
- Quasars
- Radio Telescopes
- Reflecting Telescopes
- Stellar Spectral Classes
- Telescopes
- Atoms and Radioactivity
- Fission and Fusion
- Medical Tracers
- Nuclear Reactors
- Radiotherapy
- Random Nature of Radioactive Decay
- Thickness Monitoring
- Circular Motion and Gravitation
- Applications of Circular Motion
- Centripetal and Centrifugal Force
- Circular Motion and Free-Body Diagrams
- Fundamental Forces
- Gravitational and Electric Forces
- Gravity on Different Planets
- Inertial and Gravitational Mass
- Vector Fields
- Conservation of Energy and Momentum
- Dynamics
- Application of Newton's Second Law
- Buoyancy
- Drag Force
- Dynamic Systems
- Free Body Diagrams
- Normal Force
- Springs Physics
- Superposition of Forces
- Tension
- Electric Charge Field and Potential
- Charge Distribution
- Charged Particle in Uniform Electric Field
- Conservation of Charge
- Electric Field Between Two Parallel Plates
- Electric Field Lines
- Electric Field of Multiple Point Charges
- Electric Force
- Electric Potential Due to Dipole
- Electric Potential due to a Point Charge
- Electrical Systems
- Equipotential Lines
- Electricity
- Ammeter
- Attraction and Repulsion
- Basics of Electricity
- Batteries
- Capacitors in Series and Parallel
- Circuit Schematic
- Circuit Symbols
- Circuits
- Current Density
- Current-Voltage Characteristics
- DC Circuit
- Electric Current
- Electric Generators
- Electric Motor
- Electrical Power
- Electricity Generation
- Emf and Internal Resistance
- Kirchhoff's Junction Rule
- Kirchhoff's Loop Rule
- National Grid Physics
- Ohm's Law
- Potential Difference
- Power Rating
- RC Circuit
- Resistance
- Resistance and Resistivity
- Resistivity
- Resistors in Series and Parallel
- Series and Parallel Circuits
- Simple Circuit
- Static Electricity
- Superconductivity
- Time Constant of RC Circuit
- Transformer
- Voltage Divider
- Voltmeter
- Electricity and Magnetism
- Benjamin Franklin's Kite Experiment
- Changing Magnetic Field
- Circuit Analysis
- Diamagnetic Levitation
- Electric Dipole
- Electric Field Energy
- Magnets
- Oersted's Experiment
- Voltage
- Electromagnetism
- Electrostatics
- Energy Physics
- Big Energy Issues
- Conservative and Non Conservative Forces
- Efficiency in Physics
- Elastic Potential Energy
- Electrical Energy
- Energy and the Environment
- Forms of Energy
- Geothermal Energy
- Gravitational Potential Energy
- Heat Engines
- Heat Transfer Efficiency
- Kinetic Energy
- Mechanical Power
- Potential Energy
- Potential Energy and Energy Conservation
- Pulling Force
- Renewable Energy Sources
- Wind Energy
- Work Energy Principle
- Engineering Physics
- Angular Momentum
- Angular Work and Power
- Engine Cycles
- First Law of Thermodynamics
- Moment of Inertia
- Non-Flow Processes
- PV Diagrams
- Reversed Heat Engines
- Rotational Kinetic Energy
- Second Law and Engines
- Thermodynamics and Engines
- Torque and Angular Acceleration
- Famous Physicists
- Fields in Physics
- Alternating Currents
- Capacitance
- Capacitor Charge
- Capacitor Discharge
- Coulomb's Law
- Dielectric
- Electric Field Strength
- Electric Fields
- Electric Potential
- Electromagnetic Induction
- Energy Stored by a Capacitor
- Equipotential Surface
- Escape Velocity
- Gravitational Field Strength
- Gravitational Fields
- Gravitational Potential
- Magnetic Fields
- Magnetic Flux Density
- Magnetic Flux and Magnetic Flux Linkage
- Moving Charges in a Magnetic Field
- Newton’s Laws
- Operation of a Transformer
- Parallel Plate Capacitor
- Planetary Orbits
- Synchronous Orbits
- Fluids
- Absolute Pressure and Gauge Pressure
- Application of Bernoulli's Equation
- Archimedes' Principle
- Conservation of Energy in Fluids
- Fluid Flow
- Fluid Systems
- Force and Pressure
- Force
- Conservation of Momentum
- Contact Forces
- Elastic Forces
- Force and Motion
- Gravity
- Impact Forces
- Moment Physics
- Moments Levers and Gears
- Moments and Equilibrium
- Pressure
- Resultant Force
- Safety First
- Time Speed and Distance
- Velocity and Acceleration
- Work Done
- Fundamentals of Physics
- Further Mechanics and Thermal Physics
- Bottle Rocket
- Charles law
- Circular Motion
- Diesel Cycle
- Gas Laws
- Heat Transfer
- Heat Transfer Experiments
- Ideal Gas Model
- Ideal Gases
- Kinetic Theory of Gases
- Models of Gas Behaviour
- Newton's Law of Cooling
- Periodic Motion
- Rankine Cycle
- Resonance
- Simple Harmonic Motion
- Simple Harmonic Motion Energy
- Temperature
- Thermal Equilibrium
- Thermal Expansion
- Thermal Physics
- Volume
- Work in Thermodynamics
- Geometrical and Physical Optics
- Kinematics Physics
- Air Resistance
- Angular Kinematic Equations
- Average Velocity and Acceleration
- Displacement, Time and Average Velocity
- Frame of Reference
- Free Falling Object
- Kinematic Equations
- Motion in One Dimension
- Motion in Two Dimensions
- Rotational Motion
- Uniformly Accelerated Motion
- Linear Momentum
- Magnetism
- Ampere force
- Earth's Magnetic Field
- Fleming's Left Hand Rule
- Induced Potential
- Magnetic Forces and Fields
- Motor Effect
- Particles in Magnetic Fields
- Permanent and Induced Magnetism
- Magnetism and Electromagnetic Induction
- Eddy Current
- Faraday's Law
- Induced Currents
- Inductance
- LC Circuit
- Lenz's Law
- Magnetic Field of a Current-Carrying Wire
- Magnetic Flux
- Magnetic Materials
- Monopole vs Dipole
- RL Circuit
- Measurements
- Mechanics and Materials
- Acceleration Due to Gravity
- Bouncing Ball Example
- Bulk Properties of Solids
- Centre of Mass
- Collisions and Momentum Conservation
- Conservation of Energy
- Density
- Elastic Collisions
- Force Energy
- Friction
- Graphs of Motion
- Linear Motion
- Materials
- Materials Energy
- Moments
- Momentum
- Power and Efficiency
- Projectile Motion
- Scalar and Vector
- Terminal Velocity
- Vector Problems
- Work and Energy
- Young's Modulus
- Medical Physics
- Absorption of X-Rays
- CT Scanners
- Defects of Vision
- Defects of Vision and Their Correction
- Diagnostic X-Rays
- Effective Half Life
- Electrocardiography
- Fibre Optics and Endoscopy
- Gamma Camera
- Hearing Defects
- High Energy X-Rays
- Lenses
- Magnetic Resonance Imaging
- Noise Sensitivity
- Non Ionising Imaging
- Physics of Vision
- Physics of the Ear
- Physics of the Eye
- Radioactive Implants
- Radionuclide Imaging Techniques
- Radionuclide Imaging and Therapy
- Structure of the Ear
- Ultrasound Imaging
- X-Ray Image Processing
- X-Ray Imaging
- Modern Physics
- Bohr Model of the Atom
- Disintegration Energy
- Franck Hertz Experiment
- Mass Energy Equivalence
- Nuclear Reaction
- Nucleus Structure
- Quantization of Energy
- Spectral Lines
- The Discovery of the Atom
- Wave Function
- Nuclear Physics
- Alpha Beta and Gamma Radiation
- Binding Energy
- Half Life
- Induced Fission
- Mass and Energy
- Nuclear Instability
- Nuclear Radius
- Radioactive Decay
- Radioactivity
- Rutherford Scattering
- Safety of Nuclear Reactors
- Oscillations
- Energy Time Graph
- Energy in Simple Harmonic Motion
- Hooke's Law
- Kinetic Energy in Simple Harmonic Motion
- Mechanical Energy in Simple Harmonic Motion
- Pendulum
- Period of Pendulum
- Period, Frequency and Amplitude
- Phase Angle
- Physical Pendulum
- Restoring Force
- Simple Pendulum
- Spring-Block Oscillator
- Torsional Pendulum
- Velocity
- Particle Model of Matter
- Physical Quantities and Units
- Converting Units
- Physical Quantities
- SI Prefixes
- Standard Form Physics
- Units Physics
- Use of SI Units
- Physics of Motion
- Acceleration
- Angular Acceleration
- Angular Displacement
- Angular Velocity
- Centrifugal Force
- Centripetal Force
- Displacement
- Equilibrium
- Forces of Nature Physics
- Galileo's Leaning Tower of Pisa Experiment
- Inclined Plane
- Inertia
- Mass in Physics
- Speed Physics
- Static Equilibrium
- Radiation
- Antiparticles
- Antiquark
- Atomic Model
- Classification of Particles
- Collisions of Electrons with Atoms
- Conservation Laws
- Electromagnetic Radiation and Quantum Phenomena
- Isotopes
- Neutron Number
- Particles
- Photons
- Protons
- Quark Physics
- Specific Charge
- The Photoelectric Effect
- Wave-Particle Duality
- Rotational Dynamics
- Angular Impulse
- Angular Kinematics
- Angular Motion and Linear Motion
- Connecting Linear and Rotational Motion
- Orbital Trajectory
- Rotational Equilibrium
- Rotational Inertia
- Satellite Orbits
- Third Law of Kepler
- Scientific Method Physics
- Data Collection
- Data Representation
- Drawing Conclusions
- Equations in Physics
- Uncertainties and Evaluations
- Space Physics
- Thermodynamics
- Heat Radiation
- Thermal Conductivity
- Thermal Efficiency
- Thermodynamic Diagram
- Thermodynamic Force
- Thermodynamic and Kinetic Control
- Torque and Rotational Motion
- Centripetal Acceleration and Centripetal Force
- Conservation of Angular Momentum
- Force and Torque
- Muscle Torque
- Newton's Second Law in Angular Form
- Simple Machines
- Unbalanced Torque
- Translational Dynamics
- Centripetal Force and Velocity
- Critical Speed
- Free Fall and Terminal Velocity
- Gravitational Acceleration
- Kinetic Friction
- Object in Equilibrium
- Orbital Period
- Resistive Force
- Spring Force
- Static Friction
- Turning Points in Physics
- Cathode Rays
- Discovery of the Electron
- Einstein's Theory of Special Relativity
- Electromagnetic Waves
- Electron Microscopes
- Electron Specific Charge
- Length Contraction
- Michelson-Morley Experiment
- Millikan's Experiment
- Newton's and Huygens' Theories of Light
- Photoelectricity
- Relativistic Mass and Energy
- Special Relativity
- Thermionic Electron Emission
- Time Dilation
- Wave Particle Duality of Light
- Waves Physics
- Acoustics
- Applications of Ultrasound
- Applications of Waves
- Diffraction
- Diffraction Gratings
- Doppler Effect in Light
- Earthquake Shock Waves
- Echolocation
- Image Formation by Lenses
- Interference
- Light
- Longitudinal Wave
- Longitudinal and Transverse Waves
- Mirror
- Oscilloscope
- Phase Difference
- Polarisation
- Progressive Waves
- Properties of Waves
- Ray Diagrams
- Ray Tracing Mirrors
- Reflection
- Refraction
- Refraction at a Plane Surface
- Resonance in Sound Waves
- Seismic Waves
- Snell's law
- Spectral Colour
- Standing Waves
- Stationary Waves
- Total Internal Reflection in Optical Fibre
- Transverse Wave
- Ultrasound
- Wave Characteristics
- Wave Speed
- Waves in Communication
- X-rays
- Work Energy and Power
- Conservative Forces and Potential Energy
- Dissipative Force
- Energy Dissipation
- Energy in Pendulum
- Force and Potential Energy
- Force vs. Position Graph
- Orbiting Objects
- Potential Energy Graphs and Motion
- Spring Potential Energy
- Total Mechanical Energy
- Translational Kinetic Energy
- Work Energy Theorem
- Work and Kinetic Energy

Save the explanation now and read when you’ve got time to spare.

SaveLerne mit deinen Freunden und bleibe auf dem richtigen Kurs mit deinen persönlichen Lernstatistiken

Jetzt kostenlos anmeldenNie wieder prokastinieren mit unseren Lernerinnerungen.

Jetzt kostenlos anmeldenTo be able to convert from one type of unit to another, we need to know the equivalence between both units. We can convert between units as long as both use the same basic units because they must measure the same physical property.

Consistency is needed when converting units. We cannot convert time to length, but we can translate time to frequency because both use time as a base. We can also convert power units to watts as energy per second units, and so on. Let’s look at these two examples in more detail.

We want to convert the oscillation of a pendulum in time to its frequency. The period (*T *), expressed in seconds, is the time it takes to complete one cycle of an oscillation. The frequency (*f *) is the number of occurrences of a repeating event per unit of time and is measured in *h**ertz*. The formula to convert from period to frequency is \(ƒ = \frac{1}{T}\).

The inverse of the value ‘x’ for *T* in seconds gives us the value ‘*Y’* in Hertz.

\[\frac{1}{x[seconds]} = Y[Hertz]\]

If the pendulum takes 3.2 seconds to come and go, we need to divide 1 by 3.2 seconds.

\(frecuency = \frac{1}{3.2 \space seconds}\)

This gives us 0.3125 [Hertz].

Let’s say we have a machine that consumes 60 watts of power each second. We want to convert power consumed to energy per second. The equation that links power, energy, and time is:

\[P = \frac{E}{t}\]

Here, P is the power in watts, E is the energy in joules, and t is the time it takes to consume or produce energy in seconds. If the machine’s consumption and energy production are measured each second, then 60 watts means 60 joules every second.

The relationship below expresses this better. Here, every watt unit is equivalent to a unit of Joules per second.

\[[watts] = \frac{[joules]}{1[second]}\]

Replace the ‘watts’ with 60:

\(60 \space watts = \frac{60 \space joules}{1 \space second} = 60 \space joules/second\)

Now let’s say we have a machine that produces 100 joules watts each minute. We want to know how much power is produced every second. We have to divide the amount of energy in joules by the number of seconds it took the machine to produce 100 watts.

\(\frac{100 \space joules}{60 \space seconds} = 1.67 \space joules/second\)

As we know, Joules per second is watts.

\(1.67 \space joules/second = 1.67 \space watts\)

To convert larger units to small ones, we need to multiply by a factor. If we wish to convert from different scales and units, we need to multiply by two factors to scale the number and convert between derived units.

To convert between basic units from a smaller to a larger scale, we need to multiply by a factor. If A is ten times B, we need to multiply B by 10 to obtain A. Let’s look at some examples.

We want to convert 1,234 tons to kilograms. We know that a ton is 1000 kilograms, so we can carry this out by multiplying 1,234 by 1000. This gives us 1234 kilograms.

We want to convert 0.3 metres to millimetres. We know that 1 millimetre is equal to \(1 \cdot 10 ^ {-3}\) meters, so we need to divide 0.3 by \(1 \cdot 10 ^ {-3}\), which gives us 300 millimetres.

We can also convert from metres to millimetres by multiplying by 1000, as 1 metre equals 1000 millimetres.

To convert between derived units and from a larger scale to a smaller one, we need to multiply by several factors. Consider the following example.

Convert 10 km/h to m/s.

Our calculations are more complex here. First, we need to convert 10 kilometres to metres. To convert kilometres to metres, we use the factor of \(1 \cdot 10 ^ 3\), giving us a velocity of 10000 [m/h].

\(10 \space km/h = 10 \cdot (1 \cdot 10^3) m/h = 1000 \space m/h\)

Now we need to convert from hours to seconds. This factor equals 3600, as 1 hour is equal to 60 minutes, and each minute to 60 seconds.

We must, therefore, divide 10000m by 3600s.

\(\frac{1000 \space m/h}{3600} = 2.8 \space m/s\)

The result is 2.8 m/s.

You can use a rule of thumb to calculate km/h to m/s just by dividing the number of km/h by 3.6.

If we do this at 10km/h, we obtain the same result:

\(\frac{10 \space km/h}{3.6} = 2.8 \space m/s\)

To convert smaller to larger units, we need to divide by a factor. As noted earlier, if we wish to combine conversion from different scales and units, we need to divide by two factors, one to scale the number and another to convert between derived units.

To convert between basic units from a smaller to a larger scale, we need to divide by a factor. If, for instance, A is ten times larger than B, we need to divide A by 10 to obtain B. See the following two examples:

We want to convert 23.4 m to kilometres. As one kilometre is 1000 metres, we need to divide 23.4 by 1000, which gives us 0.023 kilometres.

We wish to convert 400 kelvin to megakelvin. The prefix ‘mega’ means \(1 \cdot 10 ^ 6\), so one megakelvin is one million kelvin. Dividing 400 kelvin by 1,000,000 gives us 0.0004 megakelvin.

To convert between derived units from small to large scales, we need to use several factors. A more complex conversion from watts to kilonewton-metres per second is required, for instance, in the example below.

We have a machine that consumes 1300 watts. The prefix kilo is equivalent to \(1 \cdot 10 ^ 3\) in standard form. This means that we need to divide 1300 watts by \(1 \cdot 10 ^ 3\) to get kilowatts.

\(1300 \space watts = 1.3 \space kilowatts\)

In a second step, we need to convert kilowatts to newton-metres per second. As 1 watt is equivalent to 1 newton-metre per second, this is straightforward. 1.3 kilowatts are equal to 1.3 kilonewton-metres per second.

\(1.3 \space kilowatts = 1.3 \space kiloNewtons \cdot m/s\)

We might need to convert units from different systems, such as the imperial and SI systems. Converting temperature, volume, and length between imperial and SI units are three common operations. A simple way to convert between imperial and SI is by using weights. Multiplying the imperial or SI values by the correct weight gives us the value in the other unit system.

Figure 1. Gallons are a commonly used unit from the imperial system.

The following table lists the conversion weights for converting between the imperial and SI systems.

Imperial to SI | SI to imperial | ||

Imperial unit | Conversion weight | SI unit | Conversion weight |

1 gallon | 3.7854 litres | 1 litre | 0.264172 gallons |

1 mile | 1.60934 kilometres | 1 kilometre | 0.621371 miles |

1 foot | 0.3048 metres | 1 metre | 3.28084 feet |

1 pound | 0.453592 kilograms | 1 kilogram | 2.20462 pounds |

To convert between Fahrenheit and Celsius, we need to use the formulas below:

\(C^{0} = \frac{5(F^{0} - 32)}{9}\)

\(F^{0} = 1.8 C^0 + 32\)

The conversion of units between systems is very common in everyday life, as the imperial system and the US Customary System of units (USCS) are still widely used. See the following examples.

The outside temperature is given as 32 degrees Fahrenheit. How much is that in Celsius?

\(C^0 = \frac{5(F^0 -32)}{9}\)

Replacing F^{0} with 32, we get:

\(C^0 = 0\)

It is a cold day!

You need to refuel your rental car during your holidays in the USA. The car is from Europe, and the tank has a capacity of 40 litres. The filling station sells the fuel in gallons, which cost $3.10 (USD). How much would it cost you to fill up the tank?

First, you need to convert the 40 litres to gallons applying the unit factor weight in the table above, which tells you that 1 litre is equivalent to 0.26 gallons.

\(40 \space liters = 40 \cdot (0.26 \space gallons) = 10.4 \space gallons\)

Then, you need to multiply this by the price of $3.10.

\(10.4 \cdot 3.1 [USD] = 32.24 [USD]\)

- Converting units allows us to translate values from one type of physical quantity to another as, for instance, when we need to translate the work done by a device to the amount of energy per second used by that device to perform the work.
- Converting units between different scales helps us understand the scale of the values with which we are working as, for instance, when we convert the speed of an aeroplane from km/h to m/s.
- Unit conversion is present in all fields of science and technology.

To convert one measurement into another one, we need to make sure that both measurements use the same basic units. We also need to know the equivalence between the units used in the two measurements.

One example is to convert a measurement done in cm to meters. Both measure the same physical quantity that is length, both use the same units (meters) and then you will only need to multiply the factor that converts cm to meters or 1[cm]=0.01[m].

More about Converting Units

How would you like to learn this content?

Creating flashcards

Studying with content from your peer

Taking a short quiz

How would you like to learn this content?

Creating flashcards

Studying with content from your peer

Taking a short quiz

Free physics cheat sheet!

Everything you need to know on . A perfect summary so you can easily remember everything.

Be perfectly prepared on time with an individual plan.

Test your knowledge with gamified quizzes.

Create and find flashcards in record time.

Create beautiful notes faster than ever before.

Have all your study materials in one place.

Upload unlimited documents and save them online.

Identify your study strength and weaknesses.

Set individual study goals and earn points reaching them.

Stop procrastinating with our study reminders.

Earn points, unlock badges and level up while studying.

Create flashcards in notes completely automatically.

Create the most beautiful study materials using our templates.

Sign up to highlight and take notes. It’s 100% free.

Save explanations to your personalised space and access them anytime, anywhere!

Sign up with Email Sign up with AppleBy signing up, you agree to the Terms and Conditions and the Privacy Policy of StudySmarter.

Already have an account? Log in