What's new in the Area & Perimeter Calculator: 4 shapes and 4 length units just added
The calculator just grew in two directions at once: four shapes that were previously left out (Rhombus, Kite, Semicircle, and Annulus/Ring) are now direct options, and the length-unit list expanded from four to eight, adding yards, miles, millimeters, and kilometers. Here's exactly what each addition does, with worked examples.
What are the 4 new length units, and when would you use each?
Quick answerThe Length unit dropdown now includes yards (yd), miles (mi), millimeters (mm), and kilometers (km), alongside the existing feet, inches, meters, and centimeters — eight units in total. Pick whichever matches the numbers on your tape measure, blueprint, or map; the calculator applies the same area and perimeter formulas regardless of which unit is selected.
Each of the four additions targets a use case the original four units didn't reach well. Yards come up in landscaping, fabric, and some sports-field measurements, where feet feel too granular. Miles fit large land parcels, trail loops, or municipal boundary work, where a perimeter in feet would be an unwieldy six- or seven-digit number. Millimeters suit small technical drawings, machined parts, and craft projects where centimeters aren't precise enough. Kilometers mirror the same idea at the opposite end of the scale — large sites, regional maps, or metric-country land parcels.
How it works: select a shape, choose the unit that matches your input dimensions from the Length unit dropdown, enter your measurements, and press Calculate. The result panel and step-by-step breakdown use that same unit automatically — no separate conversion step needed.
What are the 4 new shapes, and what are their formulas?
Quick answerThe shape picker now includes Rhombus, Kite, Semicircle, and Annulus/Ring, in addition to the squares, rectangles, circles, triangles, trapezoids, and other shapes already supported. All four use straightforward formulas that are now built into the tool instead of requiring manual combination of simpler shapes.
Rhombus — a four-sided shape with all sides equal. Area = (d1 × d2) / 2, using the two diagonals. Perimeter = 4 × side.
Kite — two pairs of adjacent equal sides. Area = (d1 × d2) / 2, the same diagonal formula as a rhombus, since both shapes have perpendicular diagonals. Perimeter = 2 × (a + b), where a and b are the two distinct side lengths.
Semicircle — half a circle. Area = (π × r²) / 2. Perimeter = π × r + 2r, which includes the straight diameter edge, not just half the circumference.
Annulus / Ring — the flat area between two concentric circles. Area = π × (R² − r²), where R is the outer radius and r is the inner radius. Perimeter (both boundary circles combined) = 2 × π × (R + r).
None of these are new math — each was previously achievable by combining two or three simpler shape calculations by hand (a ring, for instance, meant subtracting one circle's area from another's). What's changed is that each is now a direct option in the Shape selector, with its own formula displayed and its own step-by-step solution, rather than a manual workaround.
Worked examples using the new shapes and units
Quick answerA rhombus tile with 10 in and 6 in diagonals covers 30 in². A semicircular window with a 2 ft radius covers about 6.28 ft². A ring-shaped garden bed with an 8 ft outer radius and a 5 ft inner radius covers about 122.52 ft². These are illustrative figures, not measurements of a real project.
Example calculations with the new shapes (hypothetical dimensions)
Shape / dimensions
Area
Perimeter
Rhombus · diagonals 10 in & 6 in, side 5.83 in
30 in²
23.32 in
Kite · diagonals 12 ft & 5 ft, sides 6.5 & 4 ft
30 ft²
21 ft
Semicircle · radius 2 ft
6.28 ft²
10.28 ft
Annulus/Ring · outer 8 ft, inner 5 ft
122.52 ft²
81.68 ft
Rectangle · 0.3 mi × 0.15 mi (using the new mile unit)
0.045 mi²
0.9 mi
Take the annulus example: a garden ring with an 8 ft outer radius and a 5 ft inner radius. Area = π × (8² − 5²) = π × (64 − 25) = π × 39 ≈ 122.52 ft². Before this shape was added directly, getting that number meant calculating the outer circle's area (π × 64 ≈ 201.06 ft²), calculating the inner circle's area separately (π × 25 ≈ 78.54 ft²), and subtracting by hand. Selecting Annulus/Ring now does that subtraction as part of the built-in step-by-step solution.
Note on units: switching the Length unit dropdown to miles, millimeters, yards, or kilometers works with every shape in the tool, not only the four new ones — a triangle, trapezoid, or regular polygon can just as easily be entered in kilometers as in feet.
Frequently asked questions
How do you calculate the area of a rhombus?
A rhombus's area is half the product of its two diagonals: Area = (d1 × d2) / 2. For example, a rhombus with diagonals of 10 ft and 6 ft has an area of (10 × 6) / 2 = 30 ft². Its perimeter is simply 4 × side, since all four sides of a rhombus are equal.
What's the difference between a rhombus and a kite for area purposes?
Both use the same diagonal-based area formula, Area = (d1 × d2) / 2, because in both shapes the diagonals are perpendicular to each other. The difference is in the sides: a rhombus has all four sides equal, so its perimeter is 4 × side, while a kite has two pairs of adjacent equal sides, so its perimeter is 2 × (a + b), where a and b are the two distinct side lengths.
How do you find the area and perimeter of a semicircle?
A semicircle's area is exactly half a full circle's area: Area = (π × r²) / 2. A semicircle with a 6 ft radius has an area of (π × 36) / 2 ≈ 56.55 ft². Its perimeter is not simply half the circumference — it also includes the straight diameter edge: Perimeter = π × r + 2r, which for the same semicircle is (π × 6) + 12 ≈ 30.85 ft.
How do you calculate the area of an annulus or ring shape?
An annulus is the flat area between two concentric circles: Area = π × (R² − r²), where R is the outer radius and r is the inner radius. For example, a ring with an 8 ft outer radius and a 5 ft inner radius has an area of π × (64 − 25) = π × 39 ≈ 122.52 ft². Its outer-plus-inner boundary length is Perimeter = 2 × π × (R + r).
Why would a calculator add units like millimeters and kilometers alongside feet and meters?
Feet, inches, meters, and centimeters cover most everyday room, yard, and lot calculations, but they don't reach either end of the scale well. Millimeters suit small technical drawings and machined parts, while kilometers suit trail distances and large land parcels. Yards and miles fill similar gaps for landscaping and long distances. Supporting all eight lets one tool handle a wider range of dimensions without a separate manual conversion step first.
Try the new shapes and units yourself — area, perimeter, formula, and a step-by-step solution, instantly in your browser.
Note: This guide is for general informational and educational purposes, not professional construction, surveying, or engineering advice. All example figures above are illustrative and not measurements of any real project — confirm exact figures with your own measurements and, where relevant, a licensed professional.