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Improved Unit Conversions in Step-by-Step Formula Calculations

Posted 6 months ago

Managing unit conversions is an important and at times complicated part of calculations for physics, chemistry and many other domains. In the past year, we've improved unit conversions and support for Wolfram|Alpha's Step-by-Step formula functionality: improving the display of our unit conversions, expanding the kinds of units we handle and providing the option to choose the target units of the solution.

Unit Choice

In the original implementation for Step-by-Step for formulas, the solutions were locked into the units for the first result in the result pod. Now Wolfram|Alpha provides a pull down menu to select any of the solutions shown in the result pod.

For example for "average velocity calculator", you can get the average velocity in a variety of different units.

unit choice

This is then reflected in the calculation for the final result so if we pick kilometers per hour Wolfram|Alpha converts the result of 1 meters per second appropriately:

unit choice results

Improved Displays

Another aspect of unit conversion we are working on is improving our displays. Our Step-by-Step calculations already have improved to make clearer the use of the factor-label method, or the application of conversion factors as fractions where unit labels cancel out until one is left with the desired units. We intend to continue to expand and improve this display format.

Another area of improvement is making clearer any unit changes within a formula, for example for a summation of units within a larger calculation. In the Step-by-Step calculation for "water hammer with slow closure" after the substitution of values into the formula we are left with a very complicated term added to a pressure. The new step text and display makes it clearer what the factors are to bring the units into alignment so we can complete the calculation:

in line unit conversions

Temperature Scales

A much more complicated example is handling units that exist as part of a scale such as temperature. Improvements in this area will be emerging later this year where the "unit conversion" is more of a formula itself. As an early example of this functionality we can look at the "wet bulb globe temperature formula" when converting to degrees Fahrenheit. Here is the final step:

temperature conversions

Wolfram|Alpha currently includes these calculations for all temperature conversions between the common temperature scales: Celsius, Fahrenheit, and Kelvins. Later this year many more formulas that use temperature such as the combined gas law and the Atkinson cycle formula will also provide Step-by-Step functionality.


We hope this expansion of Step-by-Step support is helpful in your studies. We will continue to improve our unit conversions in the coming year to expose more formulas involving temperature and expanded factor-label method.

Learn more about our expanded formula coverage here.

POSTED BY: Jason Martinez
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