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100 tools for quantities, motion, forces, energy, heat, electricity, waves, light, weather and chemistry. 100 tools with purposes, formulas and worked examples.

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Formula, calculation steps & example

All 100 tools: purposes and formulas

Centimeters to meters — Calculate centimeters to meters from the labeled values.
Output = input × 0.01
Millimeters to meters — Calculate millimeters to meters from the labeled values.
Output = input × 0.001
Kilometers to meters — Calculate kilometers to meters from the labeled values.
Output = input × 1000
Grams to kilograms — Calculate grams to kilograms from the labeled values.
Output = input × 0.001
Liters to cubic meters — Calculate liters to cubic meters from the labeled values.
Output = input × 0.001
Hours to seconds — Calculate hours to seconds from the labeled values.
Output = input × 3600
kWh to joules — Calculate kwh to joules from the labeled values.
Output = input × 3600000
Joules to kWh — Calculate joules to kwh from the labeled values.
Output = input × 2.7777777777777776e-7
Newtons to standard kilogram-force — Calculate newtons to standard kilogram-force from the labeled values.
Output = input × 0.10197162129779283
Bar to pascals — Calculate bar to pascals from the labeled values.
Output = input × 100000
Average speed — Divide traveled distance by elapsed time.
A ÷ B (A, B, C refer to the labeled entries)
Distance at constant speed — Multiply constant speed by elapsed time.
A × B (A, B, C refer to the labeled entries)
Constant-speed travel time — Solve time from distance and speed.
A ÷ B (A, B, C refer to the labeled entries)
Average acceleration — Calculate average acceleration from the labeled values.
a = (final velocity − initial velocity)/time
Constant-acceleration final velocity — Calculate constant-acceleration final velocity from the labeled values.
Final v = initial v + acceleration × time
Constant-acceleration displacement — Calculate constant-acceleration displacement from the labeled values.
Displacement = initial v×t + 0.5×a×t²
Ideal fall time — Calculate ideal fall time from the labeled values.
Time = sqrt(2×height/gravity)
Ideal impact-speed magnitude — Calculate ideal impact-speed magnitude from the labeled values.
Speed = sqrt(2×gravity×height)
RPM to angular speed — Calculate rpm to angular speed from the labeled values.
Radians/second = RPM×2π/60
Rotating-point tangential speed — Calculate rotating-point tangential speed from the labeled values.
Speed = angular speed × radius
Force from mass and acceleration — Apply Newton’s second law.
A × B (A, B, C refer to the labeled entries)
Mass from force and acceleration — Solve the mass in F=ma.
A ÷ B (A, B, C refer to the labeled entries)
Acceleration from force and mass — Solve acceleration in F=ma.
A ÷ B (A, B, C refer to the labeled entries)
Weight force — Calculate weight force from the labeled values.
Weight N = mass × gravity
Pressure from force and area — Spread perpendicular force over area.
A ÷ B (A, B, C refer to the labeled entries)
Perpendicular lever torque — Apply a force perpendicular to a lever.
A × B (A, B, C refer to the labeled entries)
Linear momentum — Multiply mass by speed magnitude.
A × B (A, B, C refer to the labeled entries)
Constant-force impulse — Multiply constant net force by its duration.
A × B (A, B, C refer to the labeled entries)
Friction magnitude model — Apply an entered friction coefficient to normal force.
A × B (A, B, C refer to the labeled entries)
Spring force magnitude — Apply a linear spring constant to displacement magnitude.
A × B (A, B, C refer to the labeled entries)
Kinetic energy — Calculate kinetic energy from the labeled values.
Energy = 0.5 × mass × speed²
Gravitational potential energy change — Calculate gravitational potential energy change from the labeled values.
Energy change = mass × gravity × height change
Work from aligned force — Multiply force by displacement along its direction.
A × B (A, B, C refer to the labeled entries)
Average power from work — Divide energy transferred by time.
A ÷ B (A, B, C refer to the labeled entries)
Energy from constant power — Multiply power by operating time.
A × B (A, B, C refer to the labeled entries)
Energy conversion efficiency — Compare useful output to input energy.
A ÷ B × 100 (A, B, C refer to the labeled entries)
Spring elastic energy — Calculate spring elastic energy from the labeled values.
Energy = 0.5 × spring constant × displacement²
Fuel energy from entered heating value — Scale a stated fuel energy per mass.
A × B (A, B, C refer to the labeled entries)
Useful output energy — Calculate useful output energy from the labeled values.
Output = input × efficiency/100
Energy not converted to useful output — Calculate energy not converted to useful output from the labeled values.
Loss = input × (1 − efficiency/100)
Celsius to Fahrenheit — Calculate celsius to fahrenheit from the labeled values.
°F = °C × 9/5 + 32
Fahrenheit to Celsius — Calculate fahrenheit to celsius from the labeled values.
°C = (°F − 32) × 5/9
Celsius to kelvin — Calculate celsius to kelvin from the labeled values.
K = °C + 273.15
Kelvin to Celsius — Calculate kelvin to celsius from the labeled values.
°C = K − 273.15
Sensible heat energy — Calculate sensible heat energy from the labeled values.
Heat = mass × specific heat × temperature change
Phase-change energy — Use mass and an entered latent heat.
A × B (A, B, C refer to the labeled entries)
Linear thermal expansion — Calculate linear thermal expansion from the labeled values.
Length change = original length × coefficient × temperature change
Steady conduction heat rate — Calculate steady conduction heat rate from the labeled values.
Heat watts = conductivity × area × ΔT / thickness
Material thermal resistance per area — Calculate material thermal resistance per area from the labeled values.
R = thickness / conductivity
SI thermal resistance to conductance — Calculate si thermal resistance to conductance from the labeled values.
U = 1 / R
Voltage from current and resistance — Apply Ohm’s law to an ideal DC resistor.
A × B (A, B, C refer to the labeled entries)
Current from voltage and resistance — Solve current using Ohm’s law.
A ÷ B (A, B, C refer to the labeled entries)
Resistance from voltage and current — Solve resistance using Ohm’s law.
A ÷ B (A, B, C refer to the labeled entries)
DC electrical power — Multiply loaded DC voltage and current.
A × B (A, B, C refer to the labeled entries)
Resistor power from current — Calculate resistor power from current from the labeled values.
Power = current² × resistance
Electric charge transferred — Multiply constant current by seconds.
A × B (A, B, C refer to the labeled entries)
Capacitor charge — Use capacitance and voltage.
A × B (A, B, C refer to the labeled entries)
Capacitor stored energy — Calculate capacitor stored energy from the labeled values.
Energy = 0.5 × capacitance × voltage²
Two series resistors — Add ideal series resistances.
A + B + … (A, B, C refer to the labeled entries)
Two parallel resistors — Calculate two parallel resistors from the labeled values.
Equivalent resistance = A×B/(A+B)
Frequency from period — Calculate frequency from period from the labeled values.
Frequency = 1 / period
Period from frequency — Calculate period from frequency from the labeled values.
Period = 1 / frequency
Wavelength from speed and frequency — Use a constant wave speed.
A ÷ B (A, B, C refer to the labeled entries)
Wave speed from wavelength and frequency — Multiply wavelength by frequency.
A × B (A, B, C refer to the labeled entries)
Echo range illustration — Calculate echo range illustration from the labeled values.
Distance = wave speed × round-trip time / 2
Oscillation count — Count cycles during a time interval.
A × B (A, B, C refer to the labeled entries)
Sound pressure level ratio — Calculate sound pressure level ratio from the labeled values.
Level dB = 20 × log10(pressure/reference)
Power ratio in decibels — Calculate power ratio in decibels from the labeled values.
dB = 10 × log10(power/reference)
Small-angle pendulum period — Calculate small-angle pendulum period from the labeled values.
Period = 2π × sqrt(length/gravity)
Mass-spring period — Calculate mass-spring period from the labeled values.
Period = 2π × sqrt(mass/spring constant)
Light frequency from wavelength — Calculate light frequency from wavelength from the labeled values.
Frequency Hz = 299792458 / (nm × 10^−9)
Vacuum light wavelength — Calculate vacuum light wavelength from the labeled values.
Wavelength nm = 299792458 / frequency × 10^9
Photon energy from frequency — Calculate photon energy from frequency from the labeled values.
Energy J = 6.62607015×10^−34 × frequency
Refractive index from light speed — Calculate refractive index from light speed from the labeled values.
Index = vacuum light speed / medium light speed
Refraction angle lesson — Calculate refraction angle lesson from the labeled values.
θ₂ = asin(n₁/n₂ × sin θ₁)
Thin-lens image distance — Calculate thin-lens image distance from the labeled values.
Image distance = 1 / (1/f − 1/object distance)
Thin-lens signed magnification — Calculate thin-lens signed magnification from the labeled values.
Magnification = −image distance/object distance
Uniform illumination over an area — Calculate uniform illumination over an area from the labeled values.
Lux = incident lumens / area
Point-source intensity factor — Calculate point-source intensity factor from the labeled values.
New/original intensity = (old/new)²
Lens focal length to diopters — Calculate lens focal length to diopters from the labeled values.
Diopters = 1 / focal length in meters
Rainfall volume over area — Convert water depth times area into liters.
A × B (A, B, C refer to the labeled entries)
Average rainfall rate — Divide recorded rainfall depth by hours.
A ÷ B (A, B, C refer to the labeled entries)
Time at a constant rainfall rate — Solve a depth accumulation interval.
A ÷ B (A, B, C refer to the labeled entries)
Rainwater collected — Calculate rainwater collected from the labeled values.
Collected liters = mm × m² × share/100
Wind gust factor — Compare peak gust with average wind speed.
A ÷ B (A, B, C refer to the labeled entries)
High/low temperature midpoint — Calculate high/low temperature midpoint from the labeled values.
Midpoint = (high + low)/2
Relative humidity from vapor pressures — Compare actual vapor pressure with saturation vapor pressure at the same temperature.
A ÷ B × 100 (A, B, C refer to the labeled entries)
Vapor pressure deficit — Subtract actual vapor pressure from saturation pressure.
A − B (A, B, C refer to the labeled entries)
Weather hPa to pascals — Calculate weather hpa to pascals from the labeled values.
Pascals = hPa × 100
Pascals to standard atmospheres — Calculate pascals to standard atmospheres from the labeled values.
Standard atmospheres = pressure Pa / 101325
Mass to moles — Divide mass by an entered molar mass.
A ÷ B (A, B, C refer to the labeled entries)
Moles to mass — Multiply amount of substance by molar mass.
A × B (A, B, C refer to the labeled entries)
Molar concentration — Divide solute moles by final solution volume.
A ÷ B (A, B, C refer to the labeled entries)
Solute moles from concentration — Multiply molar concentration by final solution volume.
A × B (A, B, C refer to the labeled entries)
Same-solute dilution volume — Calculate same-solute dilution volume from the labeled values.
Final volume = starting concentration × starting volume / target concentration
Solute mass percentage — Compare solute mass with total solution mass.
A ÷ B × 100 (A, B, C refer to the labeled entries)
Binary mixture mole fraction — Calculate binary mixture mole fraction from the labeled values.
A mole fraction = A/(A+B)
Mass-based ppm — Compute milligrams per kilogram.
A ÷ B (A, B, C refer to the labeled entries)
Ideal gas pressure — Calculate ideal gas pressure from the labeled values.
Pressure = moles × 8.31446261815324 × K / volume m³
Particles from moles — Calculate particles from moles from the labeled values.
Entities = moles × 6.02214076×10²³

Definitions and source references

Unit definitions and selected model references:

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