Moment of Inertia Converter

Moment of Inertia Converter has two tabs: the second moment of area of a cross-section (mm⁴, cm⁴, in⁴, ft⁴) and the mass moment of inertia of a body (kg·m², lb·ft², slug·ft²). It also shows how the result is calculated, step by step.

The numbered parts in Figure 1 are:

1. From box: the value you want to convert.
2. Unit button: shows the unit and opens the unit window.
3. Swap: exchanges the From and To units.
4. To box: the converted value. You can type here too.
5. Display options: significant figures, notation and digit groups.
6. Result: the conversion in large type, with a copy button.
7. Examples: common conversions, one click each.
8. Tabs: switch between area moment (I) and mass moment (J).

1. Converting a value

1. Type a value in the From box, for example 100.
2. Click the unit button under it and choose the unit, for example inch to the fourth (in⁴).
3. Click the unit button under the To box and choose the unit you want, for example millimeter to the fourth (mm⁴).
4. The converted value appears at once in the To box and in the large result panel: 100 in⁴ = 41 623 142.56 mm⁴.
5. You can also type in the To box; the From value then follows.
6. The round button between the boxes swaps the two units.

On a wide screen the From and To boxes sit side by side (Figure 1); on a phone they are stacked (Figure 2).

2. The two tabs

The tabs at the top of the Convert panel choose the quantity. Each tab keeps its own units and value.

• Area moment (I): the second moment of area of a cross-section, used in bending and buckling (mm⁴, cm⁴, in⁴, ft⁴).
• Mass moment (J): the rotational inertia of a body, used in dynamics (kg·m², lb·ft², slug·ft²). For example 1 slug·ft² = 1.355817948 kg·m².
• The two are different quantities and cannot be converted into each other.

3. Choosing a unit

Click the unit button under a value box. A window opens with every unit of the quantity, in groups; the unit in use is outlined in green.

• Search: start typing in the box at the top and the list narrows as you type (Figure 4). The best match comes first.
• You can search by symbol, by name or by another common word for the unit.
• Keyboard: ↑ and ↓ move between the units, Enter chooses, Esc closes the window.
• Clicking outside the window closes it without changing the unit.

4. Entering numbers

The value boxes accept several ways of writing a number:

5. Display options and the result

The Display box above the result sets how numbers are shown:

• Significant figures: Auto shows up to 10 digits and drops trailing zeros. Choose 3 or 4 to match the usual accuracy of engineering answers (Figure 5).
• Notation: Auto switches to scientific notation for very large or very small numbers; Plain and Scientific force one style.
• Digit groups: separates thousands with a thin space, for example 1 234 567.

The green result panel repeats the conversion in large type. Copy result copies the value with its unit, ready to paste into a report or a problem answer.

6. How it is converted

This panel writes the conversion as a chain of factors, each a ratio equal to 1. Units that cancel are struck out. Converting between two non-SI units goes through the SI unit, m⁴ (Figure 6).

• Direct factor gives one unit in terms of the other, in both directions.
• Unit definitions lists the definitions behind every factor.

7. All units

The last panel lists the same value in every unit at once, in two columns on a wide screen (Figure 7).

• The From unit is marked in blue and the To unit in green.
• Click a row to make it the To unit, or use its copy button to copy that value.

8. Theme and saved settings

The moon or sun button at the top right switches between the light and dark themes (Figure 8).

The converter remembers your last values, units and display options on this device, so it opens where you left it.

9. Units included