Simple Math

Learn to perform calculations with quantities. The library handles units automatically!

Goal: Add, subtract, multiply, and divide quantities
Time: ~10 minutes

Math with Quantities

One of mp-units' superpowers: units are handled automatically during calculations.

When you divide distance by time, you get speed (km/h) - no manual conversions needed!

Try It: Basic Operations

// ce-embed height=600 compiler=clang2110 flags="-std=c++23 -stdlib=libc++ -O3" mp-units=trunk
#include <mp-units/systems/si.h>
#include <format>
#include <iostream>

int main()
{
  using namespace mp_units;
  using namespace mp_units::si::unit_symbols;

  // Journey distances
  quantity trip1 = 6 * km;
  quantity trip2 = 2700 * m;

  // Addition: km + m = m (common unit!)
  quantity total_distance = trip1 + trip2;
  std::cout << std::format("Total distance: {}\n", total_distance);

  // Time taken
  quantity time = 2 * h;

  // Division: km / h = km/h (speed!)
  quantity average_speed = total_distance / time;
  std::cout << std::format("Average speed: {}\n", average_speed);

  // Multiplication: speed * time = distance
  quantity distance_traveled = average_speed * time;
  std::cout << std::format("Distance traveled: {}\n", distance_traveled);

  // Subtraction: km - m = m (common unit!)
  quantity difference = trip1 - trip2;
  std::cout << std::format("Difference between trips: {}\n", difference);
}

What happened:

Addition/Subtraction: Only works with compatible units (km + m ✅, km + hours ❌)
- Notice: Adding km + m automatically converted to a common unit (m)
Multiplication/Division: Creates new units automatically (km ÷ h = km/h)
Dimensional analysis: The library tracks units through all operations

Key insight: The library automatically handles unit conversions and dimensional analysis during calculations.

Valid Operations

Operation	Example	Result Unit
Addition	`120 * km + 80 * km`	`200 km`
Subtraction	`120 * km - 80 * km`	`40 km`
Division	`120 * km / (2 * h)`	`60 km/h`
Multiplication	`60 * km / h * (2 * h)`	`120 km`
Scalar multiply	`50 * km * 2`	`100 km`
Scalar divide	`100 * km / 4`	`25 km`

Common Units in Addition/Subtraction

When adding quantities with different units (like km + m above), the library picks a common unit for the result - typically the more fundamental unit:

quantity result = 1 * km + 2000 * m;  // Result: 3000 m

!!! info

When mixing different unit systems (e.g., SI km + imperial mi), the library finds a
common unit that may differ from both inputs. You'll often need to explicitly convert
to your preferred unit with `.in(unit)`. Learn more about this in
[Generic Interfaces](../type_safety/generic_interfaces.md).

Challenges

Try these in the editor above:

Calculate fuel efficiency: quantity fuel = 50 * l; then total_distance / fuel (km/L)
Multiple operations: Try (trip1 + trip2) / (time * 2)
Acceleration: quantity velocity = 30 * m / s; quantity duration = 5 * s; then velocity / duration
See compile errors: Try trip1 + time or trip1 < time - observe the compiler's error message! (We'll explore this compile-time safety in depth in Compile-Time Protection)

What You Learned?

✅ Addition/subtraction only work with compatible units
✅ Adding different units (km + m) produces a common unit result
✅ Multiplication/division create new composite quantities
✅ Dimensional analysis happens automatically
✅ Format quantities with std::format for flexible output

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