diff --git a/apps/server/src/core/base/formula/__tests__/eval.spec.ts b/apps/server/src/core/base/formula/__tests__/eval.spec.ts
new file mode 100644
index 000000000..0dbdb94f7
--- /dev/null
+++ b/apps/server/src/core/base/formula/__tests__/eval.spec.ts
@@ -0,0 +1,54 @@
+import {
+  parseRaw, resolve, evaluate, registry, isErrorCell, DEFAULT_MAX_DEPTH,
+} from "@docmost/base-formula/server";
+import "@docmost/base-formula/server"; // ensure functions/index.ts loaded (side-effect)
+import type { EvalContext, PropertyLookup, Value } from "@docmost/base-formula/server";
+
+const mkCtx = (props: Record<string, any>): EvalContext => ({
+  registry,
+  properties: new Map<string, PropertyLookup>(
+    Object.keys(props).map((k) => [k, { id: k, type: "number", typeOptions: {} }]),
+  ),
+  depth: 0,
+  maxDepth: DEFAULT_MAX_DEPTH,
+  memo: new Map(),
+});
+
+const run = (src: string, cells: Record<string, Value>): Value => {
+  const names = new Map(Object.keys(cells).map((k) => [k.replace(/^prop_/, ""), k]));
+  const { ast } = resolve(parseRaw(src), names);
+  return evaluate(ast, cells, mkCtx(cells));
+};
+
+describe("evaluate", () => {
+  it("evaluates arithmetic", () => {
+    expect(run('prop("a") + prop("b")', { prop_a: 2, prop_b: 3 })).toBe(5);
+  });
+  it("evaluates comparisons", () => {
+    expect(run('prop("a") > 0', { prop_a: 1 })).toBe(true);
+  });
+  it("short-circuits if/then", () => {
+    expect(run('if(prop("a") > 0, "pos", "neg")', { prop_a: 5 })).toBe("pos");
+    expect(run('if(prop("a") > 0, "pos", "neg")', { prop_a: -1 })).toBe("neg");
+  });
+  it("short-circuits and/or", () => {
+    expect(run('and(true, false)', {})).toBe(false);
+    expect(run('or(false, true)', {})).toBe(true);
+  });
+  it("returns null for null arithmetic", () => {
+    expect(run('prop("a") + 1', { prop_a: null })).toBe(null);
+  });
+  it("returns DIV_BY_ZERO for 1/0", () => {
+    const v = run('1 / 0', {});
+    expect(isErrorCell(v)).toBe(true);
+    if (isErrorCell(v)) expect(v.__err).toBe("DIV_BY_ZERO");
+  });
+});
+
+// TODO: unskip after Task 15 wires the function registry with round/concat.
+describe.skip("evaluate with registered functions", () => {
+  it("invokes registered functions", () => {
+    expect(run('round(1.6)', {})).toBe(2);
+    expect(run('concat("a", "b", "c")', {})).toBe("abc");
+  });
+});
diff --git a/packages/base-formula/src/eval.ts b/packages/base-formula/src/eval.ts
new file mode 100644
index 000000000..58a2c030f
--- /dev/null
+++ b/packages/base-formula/src/eval.ts
@@ -0,0 +1,106 @@
+// packages/base-formula/src/eval.ts
+import { makeErrorCell, isErrorCell } from "./error";
+import type { FormulaAST, OpCode } from "./ast";
+import type { Value, EvalContext } from "./types";
+
+export function evaluate(
+  ast: FormulaAST,
+  row: Record<string, unknown>,
+  ctx: EvalContext,
+): Value {
+  switch (ast.t) {
+    case "num":  return ast.v;
+    case "str":  return ast.v;
+    case "bool": return ast.v;
+    case "null": return null;
+    case "prop": return evalProp(ast.id, row, ctx);
+    case "op":   return evalOp(ast.op, ast.args, row, ctx);
+    case "if": {
+      const c = evaluate(ast.cond, row, ctx);
+      if (isErrorCell(c)) return c;
+      return evaluate(c === true ? ast.then : ast.else, row, ctx);
+    }
+    case "and": {
+      for (const a of ast.args) {
+        const v = evaluate(a, row, ctx);
+        if (isErrorCell(v)) return v;
+        if (v === false) return false;
+        if (v == null) return null;
+      }
+      return true;
+    }
+    case "or": {
+      for (const a of ast.args) {
+        const v = evaluate(a, row, ctx);
+        if (isErrorCell(v)) return v;
+        if (v === true) return true;
+      }
+      return false;
+    }
+    case "call": {
+      const fn = ctx.registry.get(ast.fn);
+      if (!fn) return makeErrorCell("MISSING_PROP", `unknown function ${ast.fn}`);
+      const args = ast.args.map((a) => evaluate(a, row, ctx));
+      for (const v of args) if (isErrorCell(v)) return { ...v, __err: "DEPENDENCY_ERROR" };
+      try { return fn.eval(args, ctx); }
+      catch (e) { return makeErrorCell("TYPE_MISMATCH", (e as Error).message); }
+    }
+  }
+}
+
+function evalProp(id: string, row: Record<string, unknown>, ctx: EvalContext): Value {
+  if (ctx.memo.has(id)) return ctx.memo.get(id)!;
+  const prop = ctx.properties.get(id);
+  if (!prop) return makeErrorCell("MISSING_PROP", `missing property ${id}`);
+  if (prop.type !== "formula") return normalize(row[id] ?? null);
+  // Nested formula: recurse with depth tracking.
+  if (ctx.depth >= ctx.maxDepth) return makeErrorCell("DEPTH_EXCEEDED", `max depth ${ctx.maxDepth}`);
+  const opts: any = prop.typeOptions;
+  const nested: EvalContext = { ...ctx, depth: ctx.depth + 1, memo: ctx.memo };
+  const v = evaluate(opts.ast, row, nested);
+  ctx.memo.set(id, v);
+  return v;
+}
+
+function normalize(v: unknown): Value {
+  if (v === undefined) return null;
+  if (v === null) return null;
+  if (typeof v === "number" || typeof v === "string" || typeof v === "boolean") return v;
+  if (isErrorCell(v)) return v;
+  return null;
+}
+
+function evalOp(
+  op: OpCode,
+  args: FormulaAST[],
+  row: Record<string, unknown>,
+  ctx: EvalContext,
+): Value {
+  const vs = args.map((a) => evaluate(a, row, ctx));
+  for (const v of vs) if (isErrorCell(v)) return { ...v, __err: "DEPENDENCY_ERROR" };
+  const [a, b] = vs;
+  switch (op) {
+    case "+":
+      if (typeof a === "string" || typeof b === "string") return (a == null ? "" : String(a)) + (b == null ? "" : String(b));
+      if (a == null || b == null) return null;
+      return Number(a) + Number(b);
+    case "-": return a == null || b == null ? null : Number(a) - Number(b);
+    case "*": return a == null || b == null ? null : Number(a) * Number(b);
+    case "/":
+      if (a == null || b == null) return null;
+      if (Number(b) === 0) return makeErrorCell("DIV_BY_ZERO", "division by zero");
+      return Number(a) / Number(b);
+    case "%":
+      if (a == null || b == null) return null;
+      if (Number(b) === 0) return makeErrorCell("DIV_BY_ZERO", "modulo by zero");
+      return Number(a) % Number(b);
+    case "==": return a === b;
+    case "!=": return a !== b;
+    case ">":  return a != null && b != null && (a as any) > (b as any);
+    case "<":  return a != null && b != null && (a as any) < (b as any);
+    case ">=": return a != null && b != null && (a as any) >= (b as any);
+    case "<=": return a != null && b != null && (a as any) <= (b as any);
+    case "neg": return a == null ? null : -Number(a);
+    case "not": return a == null ? null : !Boolean(a);
+  }
+}
diff --git a/packages/base-formula/src/index.server.ts b/packages/base-formula/src/index.server.ts
index 4dcc81e51..10c4b0284 100644
--- a/packages/base-formula/src/index.server.ts
+++ b/packages/base-formula/src/index.server.ts
@@ -10,3 +10,4 @@ export * from "./format";
 export { registry, register } from "./functions/registry";
 export type { FormulaFn } from "./functions/registry";
 export * from "./graph";
+export * from "./eval";