diff --git a/frontend/src/utils/grading.test.ts b/frontend/src/utils/grading.test.ts
new file mode 100644
index 0000000..628211f
--- /dev/null
+++ b/frontend/src/utils/grading.test.ts
@@ -0,0 +1,95 @@
+import { describe, it, expect } from 'vitest'
+import {
+  normalizeString,
+  normalizeLatex,
+  arraysEqualUnordered,
+  arraysEqualOrdered,
+  gradeQuestion,
+} from './grading'
+import type { Question } from '../types'
+
+describe('normalizeString', () => {
+  it('lowercases by default', () => {
+    expect(normalizeString('Hello World')).toBe('hello world')
+  })
+  it('removes accents by default', () => {
+    expect(normalizeString('café')).toBe('cafe')
+  })
+  it('removes punctuation by default', () => {
+    expect(normalizeString('Hello, world!')).toBe('hello world')
+  })
+  it('respects caseSensitive', () => {
+    expect(normalizeString('Hello', { caseSensitive: true })).toBe('Hello')
+  })
+  it('respects ignoreAccents false', () => {
+    expect(normalizeString('café', { ignoreAccents: false })).toBe('café')
+  })
+})
+
+describe('normalizeLatex', () => {
+  it('strips whitespace', () => {
+    expect(normalizeLatex('2x + 1')).toBe('2x+1')
+  })
+  it('strips left/right', () => {
+    expect(normalizeLatex('\\left(x\\right)')).toBe('(x)')
+  })
+  it('replaces cdot with *', () => {
+    expect(normalizeLatex('a\\cdot b')).toBe('a*b')
+  })
+})
+
+describe('arraysEqualUnordered', () => {
+  it('matches same elements in different order', () => {
+    expect(arraysEqualUnordered(['a', 'b'], ['b', 'a'])).toBe(true)
+  })
+  it('fails on different elements', () => {
+    expect(arraysEqualUnordered(['a', 'b'], ['a', 'c'])).toBe(false)
+  })
+  it('fails on different lengths', () => {
+    expect(arraysEqualUnordered(['a'], ['a', 'b'])).toBe(false)
+  })
+})
+
+describe('arraysEqualOrdered', () => {
+  it('matches same order', () => {
+    expect(arraysEqualOrdered(['a', 'b'], ['a', 'b'])).toBe(true)
+  })
+  it('fails on different order', () => {
+    expect(arraysEqualOrdered(['a', 'b'], ['b', 'a'])).toBe(false)
+  })
+})
+
+describe('gradeQuestion', () => {
+  it('grades multiple-choice correctly', () => {
+    const q: Question = { id: '1', type: 'multiple-choice', prompt: 'Q', answer: 'a' }
+    expect(gradeQuestion(q, 'a')).toMatchObject({ status: 'correct', correct: true })
+    expect(gradeQuestion(q, 'b')).toMatchObject({ status: 'wrong', correct: false })
+  })
+  it('grades multiple-select correctly', () => {
+    const q: Question = { id: '1', type: 'multiple-select', prompt: 'Q', answer: ['a', 'c'] }
+    expect(gradeQuestion(q, ['c', 'a'])).toMatchObject({ status: 'correct', correct: true })
+    expect(gradeQuestion(q, ['a'])).toMatchObject({ status: 'wrong', correct: false })
+  })
+  it('grades short-answer with normalization', () => {
+    const q: Question = { id: '1', type: 'short-answer', prompt: 'Q', answer: 'Paris' }
+    expect(gradeQuestion(q, 'paris')).toMatchObject({ status: 'correct', correct: true })
+  })
+  it('returns unanswered for null', () => {
+    const q: Question = { id: '1', type: 'multiple-choice', prompt: 'Q', answer: 'a' }
+    expect(gradeQuestion(q, null)).toMatchObject({ status: 'unanswered', correct: false })
+  })
+  it('grades order correctly', () => {
+    const q: Question = { id: '1', type: 'order', prompt: 'Q', answer: ['s1', 's2', 's3'] }
+    expect(gradeQuestion(q, ['s1', 's2', 's3'])).toMatchObject({ status: 'correct', correct: true })
+    expect(gradeQuestion(q, ['s1', 's3', 's2'])).toMatchObject({ status: 'wrong', correct: false })
+  })
+  it('grades match correctly', () => {
+    const q: Question = { id: '1', type: 'match', prompt: 'Q', answer: { l1: 'r1', l2: 'r2' } }
+    expect(gradeQuestion(q, { l1: 'r1', l2: 'r2' })).toMatchObject({ status: 'correct', correct: true })
+    expect(gradeQuestion(q, { l1: 'r2', l2: 'r1' })).toMatchObject({ status: 'wrong', correct: false })
+  })
+  it('grades essay as ungraded', () => {
+    const q: Question = { id: '1', type: 'essay', prompt: 'Q' }
+    expect(gradeQuestion(q, { text: 'some text' })).toMatchObject({ status: 'ungraded' })
+  })
+})
diff --git a/frontend/src/utils/grading.ts b/frontend/src/utils/grading.ts
new file mode 100644
index 0000000..878a3b8
--- /dev/null
+++ b/frontend/src/utils/grading.ts
@@ -0,0 +1,106 @@
+import type { Question, GradeResult } from '../types'
+
+interface NormalizeOpts {
+  caseSensitive?: boolean
+  ignoreAccents?: boolean
+  ignorePunctuation?: boolean
+}
+
+export const normalizeString = (s: unknown, opts: NormalizeOpts = {}): string => {
+  if (s == null) return ''
+  let out = String(s)
+  if (!opts.caseSensitive) out = out.toLowerCase()
+  if (opts.ignoreAccents !== false) {
+    out = out.normalize('NFD').replace(/[̀-ͯ]/g, '')
+  }
+  if (opts.ignorePunctuation !== false) {
+    out = out.replace(/[.,/#!$%^&*;:{}=\-_`~()¿?¡!'"]/g, '')
+  }
+  return out.replace(/\s+/g, ' ').trim()
+}
+
+export const normalizeLatex = (s: unknown): string => {
+  if (s == null) return ''
+  return String(s)
+    .replace(/\s+/g, '')
+    .replace(/\\left|\\right/g, '')
+    .replace(/\\,|\\;|\\:|\\!|\\ /g, '')
+    .replace(/\{([^{}])\}/g, '$1')
+    .replace(/\\cdot/g, '*')
+    .replace(/\\times/g, '*')
+    .replace(/\\ln/g, 'ln')
+    .replace(/\\log/g, 'log')
+    .toLowerCase()
+}
+
+export const arraysEqualUnordered = (a: unknown[], b: unknown[]): boolean => {
+  if (!Array.isArray(a) || !Array.isArray(b)) return false
+  if (a.length !== b.length) return false
+  const sa = [...a].sort()
+  const sb = [...b].sort()
+  return sa.every((v, i) => v === sb[i])
+}
+
+export const arraysEqualOrdered = (a: unknown[], b: unknown[]): boolean => {
+  if (!Array.isArray(a) || !Array.isArray(b)) return false
+  if (a.length !== b.length) return false
+  return a.every((v, i) => v === b[i])
+}
+
+export const gradeQuestion = (q: Question, userAnswer: unknown): GradeResult => {
+  if (userAnswer == null) return { status: 'unanswered', correct: false, points: 0 }
+  const pts = q.points ?? 1
+
+  switch (q.type) {
+    case 'multiple-choice': {
+      const ok = userAnswer === q.answer
+      return { status: ok ? 'correct' : 'wrong', correct: ok, points: ok ? pts : 0 }
+    }
+    case 'multiple-select': {
+      const ok = arraysEqualUnordered(userAnswer as unknown[], (q.answer as string[]) ?? [])
+      return { status: ok ? 'correct' : 'wrong', correct: ok, points: ok ? pts : 0 }
+    }
+    case 'short-answer':
+    case 'translation': {
+      const opts: NormalizeOpts = {
+        caseSensitive: q.caseSensitive === true,
+        ignorePunctuation: q.ignorePunctuation !== false,
+        ignoreAccents: q.ignoreAccents !== false,
+      }
+      const target = normalizeString(userAnswer, opts)
+      const accepted = [q.answer as string, ...(q.acceptedForms ?? [])]
+        .filter(Boolean)
+        .map((a) => normalizeString(a, opts))
+      const ok = accepted.includes(target)
+      return { status: ok ? 'correct' : 'wrong', correct: ok, points: ok ? pts : 0 }
+    }
+    case 'math-input': {
+      const target = normalizeLatex(userAnswer)
+      const accepted = [q.answer as string, ...(q.acceptedForms ?? [])].filter(Boolean).map(normalizeLatex)
+      const ok = accepted.includes(target)
+      return { status: ok ? 'correct' : 'wrong', correct: ok, points: ok ? pts : 0 }
+    }
+    case 'match': {
+      const answer = (q.answer as Record<string, string>) ?? {}
+      const given = (userAnswer as Record<string, string>) ?? {}
+      const keys = Object.keys(answer)
+      if (keys.length === 0) return { status: 'unanswered', correct: false, points: 0 }
+      const allOk = keys.every((k) => given[k] === answer[k])
+      return { status: allOk ? 'correct' : 'wrong', correct: allOk, points: allOk ? pts : 0 }
+    }
+    case 'order': {
+      const ok = arraysEqualOrdered(userAnswer as unknown[], (q.answer as string[]) ?? [])
+      return { status: ok ? 'correct' : 'wrong', correct: ok, points: ok ? pts : 0 }
+    }
+    case 'essay': {
+      const val = userAnswer as { selfGrade?: number }
+      if (val?.selfGrade != null) {
+        const g = val.selfGrade
+        return { status: g >= 0.5 ? 'correct' : 'wrong', correct: g >= 0.5, points: Math.round(pts * g) }
+      }
+      return { status: 'ungraded', correct: false, points: 0 }
+    }
+    default:
+      return { status: 'unanswered', correct: false, points: 0 }
+  }
+}