diff --git a/packages/components/src/font-size-picker/index.js b/packages/components/src/font-size-picker/index.js
index 1f8bf8e02b06bd..6f6f2a0d137a58 100644
--- a/packages/components/src/font-size-picker/index.js
+++ b/packages/components/src/font-size-picker/index.js
@@ -126,10 +126,14 @@ function FontSizePicker(
 							if ( 0 === parseFloat( nextSize ) || ! nextSize ) {
 								onChange( undefined );
 							} else {
-								onChange( nextSize );
+								onChange(
+									hasUnits
+										? nextSize
+										: parseInt( nextSize, 10 )
+								);
 							}
 						} }
-						units={ units }
+						units={ hasUnits ? units : false }
 					/>
 				) }
 				<Button
diff --git a/packages/components/src/font-size-picker/test/index.js b/packages/components/src/font-size-picker/test/index.js
new file mode 100644
index 00000000000000..f26d6144f930c9
--- /dev/null
+++ b/packages/components/src/font-size-picker/test/index.js
@@ -0,0 +1,136 @@
+/**
+ * External dependencies
+ */
+import { render, fireEvent, screen } from '@testing-library/react';
+
+/**
+ * Internal dependencies
+ */
+import FontSizePicker from '../';
+
+const getUnitSelect = () =>
+	document.body.querySelector( '.components-unit-control select' );
+const getUnitLabel = () =>
+	document.body.querySelector( '.components-unit-control__unit-label' );
+
+describe( 'FontSizePicker', () => {
+	describe( 'onChange values', () => {
+		it( 'should not use units when the initial value is a number', () => {
+			let fontSize = 12;
+			const setFontSize = jest.fn(
+				( nextSize ) => ( fontSize = nextSize )
+			);
+
+			render(
+				<FontSizePicker value={ fontSize } onChange={ setFontSize } />
+			);
+
+			const unitSelect = getUnitSelect();
+			const unitLabel = getUnitLabel();
+			const input = screen.getByLabelText( 'Custom', {
+				selector: 'input',
+			} );
+
+			input.focus();
+			fireEvent.change( input, { target: { value: 16 } } );
+
+			expect( unitSelect ).toBeFalsy();
+			expect( unitLabel ).toBeTruthy();
+			expect( fontSize ).toBe( 16 );
+		} );
+
+		it( 'should use units when the initial value has a unit', () => {
+			let fontSize = '12px';
+			const setFontSize = jest.fn(
+				( nextSize ) => ( fontSize = nextSize )
+			);
+
+			render(
+				<FontSizePicker value={ fontSize } onChange={ setFontSize } />
+			);
+
+			const unitSelect = getUnitSelect();
+			const unitLabel = getUnitLabel();
+			const input = screen.getByLabelText( 'Custom', {
+				selector: 'input',
+			} );
+
+			input.focus();
+			fireEvent.change( input, { target: { value: 16 } } );
+
+			expect( unitSelect ).toBeTruthy();
+			expect( unitLabel ).toBeFalsy();
+			expect( fontSize ).toBe( '16px' );
+		} );
+
+		it( 'should not use units when fontSizes size values are numbers', () => {
+			let fontSize;
+			const fontSizes = [
+				{
+					name: 'Small',
+					slug: 'small',
+					size: 12,
+				},
+			];
+			const setFontSize = jest.fn(
+				( nextSize ) => ( fontSize = nextSize )
+			);
+
+			render(
+				<FontSizePicker
+					fontSizes={ fontSizes }
+					value={ fontSize }
+					onChange={ setFontSize }
+				/>
+			);
+
+			const unitSelect = getUnitSelect();
+			const unitLabel = getUnitLabel();
+			const input = screen.getByLabelText( 'Custom', {
+				selector: 'input',
+			} );
+
+			input.focus();
+			fireEvent.change( input, { target: { value: 16 } } );
+
+			expect( unitSelect ).toBeFalsy();
+			expect( unitLabel ).toBeTruthy();
+			expect( fontSize ).toBe( 16 );
+		} );
+
+		it( 'should use units when fontSizes size values have units', () => {
+			let fontSize;
+			const fontSizes = [
+				{
+					name: 'Small',
+					slug: 'small',
+					size: '12px',
+				},
+			];
+			const setFontSize = jest.fn(
+				( nextSize ) => ( fontSize = nextSize )
+			);
+
+			render(
+				<FontSizePicker
+					fontSizes={ fontSizes }
+					value={ fontSize }
+					onChange={ setFontSize }
+				/>
+			);
+
+			const unitSelect = getUnitSelect();
+			const unitLabel = getUnitLabel();
+			const input = screen.getByLabelText( 'Custom', {
+				selector: 'input',
+			} );
+
+			input.focus();
+			fireEvent.change( input, { target: { value: 16 } } );
+
+			expect( unitSelect ).toBeTruthy();
+			expect( unitLabel ).toBeFalsy();
+			expect( fontSize ).toBe( '16px' );
+		} );
+	} );
+} );